Preheat oven to 325 degrees F (165 degrees C). Grease an 8x8-inch square pan.

Sift flour, baking powder, and salt together in a bowl.

Beat sugar and butter together in a large bowl with an electric mixer until light and fluffy. Beat in eggs until smooth batter forms; beat in chocolate and vanilla extract. Stir flour mixture in just until incorporated; fold in walnuts. Spread batter into prepared square pan.

Bake in preheated oven until top is dry and edges have started to pull away from the sides of the pan, 40 to 45 minutes. Cool completely in square pan, about 30 minutes; cut into 9 squares.