Make the strawberry icing: Whisk the softened butter with a hand whisk or stand mixer until light and fluffy, then sift in confectioners sugar until well combined and there are no lumps remaining. Whisk in the strawberry ice cream, and salt to taste, until combined. I use approximately 1/8 teaspoon of salt. Taste the frosting, if it is too sweet, add more salt. Cover and chill the icing in the freezer for at least 30 minutes while you make the cupcakes.
Preheat the oven to 350°F (177°C). Line muffin pan with 12 cupcake liners and place one cookie at the bottom of each liner. Cut the tops off of 12 medium strawberries and place whole strawberries on each cookie with the pointy side up. The strawberries should be cut so that they just reach the top of the cupcake liner. Set aside.
Make the cupcake batter: In a medium bowl, whisk together flour, baking powder, and salt. In stand mixer or medium bowl with a hand mixer, cream the butter and sugar together until light and fluffy. Add the egg, buttermilk, and vanilla and mix well. Finally, add the dry ingredients to the wet ingredients, 1/3 at a time. Mix until well combined and you have a smooth batter.
Add the batter to a piping bag fitted with a piping tip and pipe the batter around the strawberries, filling the cupcake liners approximately 3/4 full. Do not over-fill. Alternatively, the batter can be spooned into the cupcake liners. Tap the tray on the counter to level the batter.
Bake cupcakes for 22-24 minutes at 350°F (177°C), or until a toothpick inserted into the cupcake comes out clean.
Transfer cupcakes to a cooling rack and allow to cool to room temperature, about 30 minutes.
When cupcakes are cooled, they are ready to be frosted however you prefer. I used a 1A Wilton tip and a piping bag. Sprinkle with decorative sugar or sprinkles.