Preheat the oven to 325°F and line a 12-cavity cupcake tin with paper liners.
In a large mixing bowl, combine ½ cup unsalted butter, ⅔ cup sweetened condensed milk, ¼ cup granulated sugar, 1 large egg, 1 teaspoon vanilla extract, and ½ teaspoon salt. Beat on high until mixed and thickened, about 3 minutes.
Add the 1 cup all-purpose flour, 1 teaspoon baking powder, and ¼ teaspoon baking soda and continue beating on high until combined. It will appear slightly grainy/separated at this point.
Add ¼ cup whole milk and beat until the batter is smooth, about 4 minutes.
Divide the batter evenly amongst the muffin cups. Sprinkle the tops of the batter with 2 tablespoons mini chocolate chips.
Bake for 20 to 25 minutes or until the cupcakes are golden brown.
Remove from the oven and let cool for about 5 minutes in the pan, then transfer to a cooling rack to cool completely.
While the cupcakes cool, prepare the frosting by chopping 6 ounces semi-sweet chocolate and adding it to a small microwavable bowl, and microwaving at 30-second intervals, stirring between each one, until the chocolate is fully melted. Cool for a few minutes before using.
In a medium mixing bowl, cream ¾ cup unsalted butter until smooth.
Add the slightly cooled melted chocolate and ¼ cup sweetened condensed milk and continue beating until it is very smooth.
Add ¾ cup powdered sugar and continue beating until the icing is fully combined.
Pipe (or spread) the icing onto the cooled cupcakes, leaving a little well in the middle on top.
Add a ½ teaspoon of the sweetened condensed milk to the well on top of the frosting. Top with mini chocolate chips and Mini chocolate chip cookies .