Preheat oven to 350°F. Line a muffin tin with liners. Set aside.

In a large bowl, whisk together flour, baking powder, salt, and sugar.

Make a well in the center of the bowl and add in butter, half and half, egg, yogurt, and vanilla extract.

Using an electric mixer, mix the wet ingredients until well combined, then gradually add the dry ingredients, mixing until incorporated. Be sure to scrape down the sides of the bowl as needed.

Using a measuring cup or ice cream scoop, add about ¼ cup of batter to each cupcake liner.

Bake on the middle rack for about 18-20 minutes or until a toothpick inserted into the center comes out clean or with moist crumbs clinging to it.

Remove the cupcakes from the pan and place them on a wire rack.

While the cupcakes cool, make the frosting by adding the powdered sugar to a large bowl.

Mix in the butter until combined and crumbly.

Mix in 2 tablespoons of half and half. If you need more add in more a teaspoon at a time until desired texture is reached.

Mix in vanilla extract and salt (if using unsalted butter).

Place frosting in a piping bag and pipe onto cooled cupcakes.