Bring milk and butter to a simmer in a saucepan over medium-low heat. Continue to cook, stirring often, until the milk has reduced to half and thickened, about 20 minutes. Remove from heat, stir in the 1/4 cup coconut, and allow to cool a bit before pouring into a buttered bowl. Chill in the refrigerator until cold, about 2 hours.

With buttered or oiled hands, form milk mixture into tablespoon-sized balls, and roll in coconut flakes. Stick a clove into each beijinho as decoration.