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Grease and flour a 9-inch tart pan with removable sides.
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Preheat the oven to 350 degrees F.
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Melt the butter in a bowl set over simmering water.
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Add 2 cups of the chocolate chips, remove from the heat, and stir until the chocolate melts.
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Set aside to cool completely.
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In the bowl of an electric mixer fitted with the paddle attachment, beat the eggs, sugar, coffee, and vanilla on medium-high speed until light and fluffy, about 3 minutes. Stir in the cooled chocolate.
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In a medium bowl, combine the flour, baking powder, salt, 1 cup of the chocolate chips, and the walnuts.
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Fold the flour mixture into the batter until just combined.
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Pour into the pan and bake for 35 to 40 minutes, until the center is puffed (the top may crack).
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The inside will still be very soft.
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Cool to room temperature before removing the sides of the tart pan.
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Melt the remaining 1/4 cup of chocolate chips with the heavy cream and drizzle on the tart.