Preheat oven to 350°F (175°C) and line a 12-cup muffin tin with paper liners.
In a medium bowl, whisk together the flour, baking powder, and salt.
In a large bowl or stand mixer, cream 1/2 cup butter and granulated sugar until light and fluffy, approximately 3 minutes.
Add the egg and 1.5 teaspoons vanilla extract, beating until fully incorporated.
Gradually add the dry ingredients to the wet ingredients, alternating with the milk, beginning and ending with the dry ingredients. Mix until just combined.
Gently fold in the 1/3 cup rainbow sprinkles using a spatula.
Divide the batter evenly among the cupcake liners, filling each about 2/3 full.
Bake for 18 to 20 minutes, or until a toothpick inserted into the center comes out clean.
Transfer cupcakes to a wire rack to cool completely before frosting.
Prepare the frosting by beating the softened butter until creamy, then gradually adding powdered sugar, heavy cream, and vanilla extract until smooth.
Pipe or spread the frosting onto the cooled cupcakes and top with additional sprinkles.