Combine 2 tablespoons each butter, beef and chicken stock in a large skillet.  Place over medium-high heat, add the chopped broccoli and cook until soft.  Purée in blender or food processor in 3 batches, adding at least 1/2 cup
stock with each batch. Transfer to a large saucepan or Dutch oven and add remaining stock. Heat through, stirring occasionally. Cover and keep warm over low heat.
Heat 4 tablespoons butter in skillet and in it sauté the mushrooms and leeks.  Add to soup. Combine the wine, shallot, and basil in a heavy medium saucepan. Reduce over medium heat until all liquid evaporates, watching carefully to avoid scorching.
Meanwhile, heat half-and-half and 1 cup whipping cream in small saucepan until just hot. Whisking constantly, add cream in slow, steady stream to shallot-basil mixture and cook over medium heat until reduced by 1/3.
Whisk cream mixture into warm soup.  (At this point, soup can be cooled
and frozen for future use.)
When ready to serve, reheat soup just to simmering point.  Fold in 1/4 cup whipping cream and salt and pepper to taste.  Makes 2 1/2 quarts.
 

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