For 2 pounds + 6 1/2 ounces (1,080 g); about 6 cups

“For this buttercream, the buttercream base is a crème anglaise (English custard), but prepared with an unusually high proportion of egg yolks and sugar or, equivalently, a very low proportion of milk. The proportions make the preparation more delicate than an ordinary crème anglaise, and the result is a hair less elegant than our French buttercream. However, this method makes it possible for you to incorporate coffee flavor in a way that is superior to anything possible with other types of buttercream.
The problem is that to add sufficient coffee flavor to buttercream after the fact requires a very strong coffee extract in order to avoid adding too much water, which would make the cream curdle. The only practical way to make such a strong extract is to dissolve instant coffee in the minimum possible amount of boiling water. It should come as no surprise that the resulting buttercream tastes like instant coffee as opposed to real coffee.
With the custard buttercream base, you can incorporate the coffee flavor from the outset by steeping coarsely crushed coffee beans in the milk before straining the milk and using it in the custard. The result is a buttercream with a freshly brewed coffee taste.
The custard buttercream base also has a second advantage. If you feel uncomfortable about working with hot sugar syrups, then this method may be a
less threatening alternative. If you prefer to prepare your basic buttercream using the custard base method, simply follow this recipe, eliminating the coffee and step
1 and reducing the quantity of milk to 3/4 cup (1.8 dL)."

3/4 cup (1 3/4 ounces; 50 g) espresso coffee beans
1 cup {2.4 dL) milk
1 1/2 cups (10 1/2 ounces; 300 g) granulated sugar
8 large egg yolks, at room temperature
2 2/3 cups (1 pound + 5 ounces; 600 g) unsalted butter, softened

Equipment
Mortar and pestle
Electric mixer, preferably a stand mixer equipped with both wire whip
and flat beater

1.  Coarsely crush the espresso beans in a mortar and pestle, processing in small batches so that none of the coffee is crushed finely. Combine the crushed espresso beans with the milk in a small saucepan and bring to a simmer. Remove from the heat, cover, and let steep for 10 minutes. Strain through a fine sieve, pressing down on the beans to extract as much milk as possible. You should have about 3/4 cup (1.8 dL) of espresso-flavored milk. If necessary, add a little milk to get back up to 3/4 cup (1.8 dL). Discard the coffee grounds and rinse out the sieve so it will be ready to use again for straining the custard.

2.  Combine the espresso-flavored milk with 1/4 cup (50 g) of the sugar in a heavy 1-quart (1-L) saucepan and bring to a simmer.

3.  Meanwhile, combine the egg yolks with the remaining sugar in a mixing bowl and beat with a wire whisk until smooth and lemon-colored. Pour in about half of the hot milk, whisking constantly. Pour this mixture back into the saucepan and stir until thoroughly blended.

4.  Place the saucepan over medium heat and, stirring constantly with a wooden spatula, bring the custard almost to a simmer.  Reduce the heat to low and cook, stirring constantly with the spatula, until the custard thickens and coats the spatula heavily. (When you draw a line across the back of the custard-coated spatula with your fingertip, the custard should not flow back over the line. Reduce the heat to the lowest possible setting (moving the saucepan to the side of the burner as needed) and keep the mixture hot, again stirring constantly, for 4 minutes to pasteurize it.

5.  Immediately strain the custard through the fine sieve into the bowl of the mixer. Beat the custard with the wire whip at medium speed until it is light and cool. This is the buttercream base.

6.  Gradually beat in the softened butter at medium speed, using the flat beater if your mixer has one. When all of the butter has been added, beat the buttercream vigorously to make it as slight as possible.

7.  Use the buttercream right away, or refrigerate it for later use.

Note on quantity – This recipe produces a fairly large quantity of buttercream. Unfortunately, it would be very difficult to prepare a smaller quantity of the custard base. If you do not have a stand mixer with a flat beater, you may want to divide the custard base in half and process each half separately following step 6 with half of the butter.

Storage – Covered airtight for up to 1 week in the refrigerator. Before using, let the buttercream soften at room temperature. Then beat it vigorously with a wooden spatula or the flat beater of the mixer to make it smooth, spreadable, and light.
Or divide the buttercream into quantities suitable for the desserts you expect to make and freeze for up to 3 months. A typical gâteau requires 1 1/2 to 2 cups (260 to 425 g) of buttercream for filling and frosting. Defrost overnight in the refrigerator, then proceed as for refrigerated buttercream.