Cream butter and sugar: In a stand mixer or large bowl, cream the softened butter and sugar together until light and fluffy, about 3 minutes. Beat in the milk and vanilla extract.
Incorporate dry ingredients: Gradually stir in the flour until just combined. Fold in the finely chopped candied cherries and pecans.
Shape and coat: Divide the dough in half. Form each half into a log about 2 inches in diameter. Spread the flaked coconut on a flat surface and roll each log in the coconut until evenly coated.
Chill the dough: Wrap each log tightly in wax paper [or plastic wrap] and chill in the refrigerator for [at least 2 hours], or until completely firm.
Slice and bake: Preheat oven to 375°F (190°C). Cut the chilled logs into [1/4-inch thick] slices. Place [1 inch apart] on an ungreased baking sheet and bake for 10 minutes, or until the coconut edges are golden brown.