Once the milk chocolate is melted, let it sit at room temp for 10 minutes before mixing it into the remaining frosting on a low speed. It should still be fully liquid, but not as warm to the touch. This will prevent it from melting the butter in the frosting and throwing off the consistency of the frosting. Mix until the chocolate is fully incorporated and the
desired consistency for the frosting is reached. Cover with plastic wrap to prevent crusting and set aside.