Gather the ingredients. Allow the butter and egg to come up to nearly room temperature.
Preheat the oven to 350°F.
Line your cookie sheets with parchment paper.

Drain the maraschino cherries, but save the juice!

Whisk the flour and cocoa together in a bowl.

Use a hand-held mixer to beat the butter until a little creamy (about 45 seconds).

Add the sugar, baking powder, baking soda, and salt. Beat until well combined.

Make the fudgy frosting. In a saucepan, combine the sweetened condensed milk with the chocolate pieces.

Melt the chocolate and condensed milk over low heat, stirring constantly. The mixture will become thick. As soon as everything is melted, remove the pot from the heat.
Add 2 teaspoons of the reserved maraschino cherry juice, and stir well. If the mixture is still far too thick to work with, continue adding the cherry juice 1 teaspoon at a time until you reach a spreadable consistency.

Form 1 inch diameter balls of dough, and place them approximately 2 inches apart on an ungreased cookie sheet.

Use your thumb to create an indentation in each of the balls.
To be more consistent, I used the melon baller tool, and then used a damp finger to press down the little nub that formed from the tool’s hole.