Preheat oven to 350 degrees. Butter and flour a 12-cup muffin pan, or use liners. Combine flour, baking powder, and 3/4 teaspoon salt. In a large bowl, using an electric mixer, beat granulated sugar and 1/2 cup butter until light and fluffy. Beat in eggs, one at a time. Beat in 1 teaspoon vanilla. With mixer on low, beat in flour mixture in two parts, alternating with 1/2 cup milk.
Divide batter among prepared muffin cups. Bake until a toothpick inserted in center of a cupcake comes out clean, about 20 minutes. Let cool in pan 5 minutes. Transfer to a wire rack to cool completely.
Meanwhile, whisk together confectioners' sugar, cocoa, and 1/4 teaspoon salt. In a large bowl, using an electric mixer, beat 1/2 cup butter until light and fluffy. With mixer on low, gradually add cocoa mixture, scraping down side of bowl as necessary. Gradually beat in 2 tablespoons milk and 1/2 teaspoon vanilla. Beat frosting until light and fluffy, about 30 seconds.
Using a paring knife, cut a 1-inch-deep piece from the top of each cupcake (do not discard). Fill each hole with 1 teaspoon jam and replace cutout pieces. Frost cupcakes and top with raspberries.