Preheat an oven to 400 degrees F (200 degrees C). Grease a 9-inch pie pan.
Beat the 1 3/4 sticks butter and 2/3 cup sugar with an electric mixer in a large bowl until light and fluffy. Whisk the 2/3 cup flour, almond meal, and 1 teaspoon baking powder together in a large bowl. Add the butter mixture and 2 teaspoon vanilla to the flour mixture; mix until soft. Chill in refrigerator for 5 minutes. Press the dough into the prepared pie pan.
Bake in the preheated oven until lightly golden in color, 15 to 20 minutes. Reduce the oven temperature to 350 degrees F (180 degrees C).
While the crust cooks, beat the egg and 3 1/2 tablespoons sugar in a large bowl until light and fluffy. Add the 7 tablespoons butter, almond paste, 1 teaspoon vanilla, 3 1/2 tablespoons flour, and 1 teaspoon baking powder and mix well. Pour the mixture into the baked pie crust.
Bake in the oven at 350 degrees F (180 degrees C) until the surface of the pie filling is firm, 30 to 40 minutes.