Preheat oven to 350 degrees F (175 degrees C). Grease a 9-inch pie plate.
Combine 1/2 cup butter and 3 tablespoons sugar in a bowl; beat with an electric mixer until creamy. Beat in 1 egg until well blended. Beat in flour and baking powder. Chill crust mixture for 30 minutes.
Spread crust mixture into the greased pie plate.
Combine cottage cheese, 1/2 cup sugar, 2 eggs, 1/3 cup melted butter, almonds, sour cream, lemon juice, lemon zest, and vanilla extract in a blender; blend until smooth. Pour over crust in the pie plate.
Bake in the preheated oven until set, about 40 minutes.