Chocolate Marshmallow Surprise Cookies

1 cube real butter, softened
1 cup sugar
1 egg
1/2 cup whole milk
1 tsp. vanilla
1-3/4 cups flour
3/4 cup cocoa powder
1/2 tsp. baking soda
1/4 tsp. salt
12 large marshmallows, cut in half horizontally

Preheat oven to 375 degrees.  Mix butter and sugar until well-combined. Add egg, milk, and vanilla, mixing well.  Add dry ingredients and mix on lower speed until well-combined. Using small cookie scoop (1-3/4"), drop dough in mounds on parchment-covered baking sheet.  Bake for 8 minutes and remove from oven.  Press 1/2 a marshmallow, cut-side down, into the top of each cookie.  Return pan to oven and bake for 2 more minutes.  Cool completely before frosting.

Frosting
With mixer, combine:
2 cups powdered sugar
4 Tbl. butter, melted and cooled
1/4 cup cocoa powder
1/4 cup milk
1/4 tsp. vanilla

Carefully spread a dollop of frosting over the top of each cooled cookie, covering marshmallow completely.  Allow to set before stacking.