In large mixing bowl, beat butter on medium speed until smooth. Melt milk chocolate chips (in microwave, heat 30 seconds; stir; repeat cycle until mostly melted) and cool slightly. Add to the butter.
Gradually add 2 cups of the powdered sugar, beating well. Slowing beat in the milk and vanilla. Gradually beat in remaining amount of powdered sugar. Beat in additional milk if needed until frosting reaches spreading consistency.
**NOTE** You can cut this recipe in half and it makes just enough for a batch of 24 cupcakes. Even cutting it in half, I still used a full cup milk chocolate chips...just because I'm good like that. :)