In a medium mixing bowl, use a hand mixer on low-speed to combine the milk and sugar until the sugar is dissolved, about 1 to 2 minutes. Stir in the heavy cream, and vanilla.
Turn the ice cream/gelato machine on; pour the mixture into freezer bowl, and let mix until thickened, about 20 to 25 minutes.
Five minutes before mixing is completed, add the Amarena cherries and let mix in completely. The ice cream will have a soft, creamy texture. If a firmer consistency is desired, transfer the ice cream to an airtight container and place in freezer for about 2 hours. Remove from freezer about 15 minutes before serving.