Prep: Preheat oven to 350°F. Line a 9x5" loaf pan with parchment paper and set aside.
Mix dry ingredients: In a medium bowl, stir together flour, baking powder, baking soda, and salt. Set aside.
Cream butter and sugar: To a large mixing bowl, add the softened butter. Use an electric hand mixer to beat the butter until it becomes very creamy and pale in colour. Add the sugar and beat together until creamy and fluffy, about 3 minutes.
Mix in eggs: Add one egg at a time, mixing after each addition. Add the vanilla extract and mix until combined.
Finish the batter: Add the flour mixture and mix on low speed until it's half combined. Pour in the milk and continue mixing until the batter is smooth. Don't overmix.
Fold in raspberries: Add the raspberries and gently fold them into the batter with a spatula just enough to distribute them. Don't overmix or the raspberry juices will bleed into the batter.
Fill pan: Transfer the batter to your lined pan and smooth the surface with a spatula.
Bake: Bake for 65-70 minutes or until a toothpick inserted in the middle comes out clean and not too wet. Let the pan cool on a wire rack for at least 30 minutes. Run an offset spatula around any edges of the pan that weren't lined with parchment paper, if needed. Lift the cake out of the pan with the parchment paper wings and let it cool completely on a wire rack before adding the frosting.