In a food processor, whirl walnuts, pine nuts, and 1/2 cup sugar until nuts are coarsely ground. Pour into a 9-inch tart pan with removable rim. In a 2-cup glass measure, melt 1/4 cup butter in a microwave oven at full power (100%), 20 to 30 seconds. Add melted butter to nut mixture and rub in with your fingers to blend. Press mixture evenly over bottom and up sides of pan. Set pan on a foil-lined 12- by 15-inch baking sheet.
Bake in a 325° regular or convection oven until crust begins to brown around edges, 20 to 30 minutes.
Meanwhile, chop half the chocolate into 1/2-inch chunks and set aside. Finely chop remaining chocolate.
In the glass measure, combine remaining 1/4 cup butter, cut into small pieces, with finely chopped chocolate. Heat in a microwave oven at half power (50%) until chocolate is soft, 30 to 45 seconds. Stir until mixture is smooth.
In a bowl with a mixer on high speed, beat egg yolks, remaining 3 tablespoons sugar, cognac, and almond extract until mixture turns pale yellow, about 3 minutes. Add chocolate-butter mixture and beat to blend. Stir in coarsely chopped chocolate. Scrape into warm nut crust.
Bake in a 325° regular or convection oven until filling barely jiggles when pan is gently shaken, about 15 minutes. Set on a rack until warm or cool.
To serve, remove rim; dust tart lightly with cocoa and cut into wedges.