Heat oven to 350℉/177℃.
Line 2 sheet pans with parchment paper. Set aside.
With an electric mixer, cream butter and sugar.
Beat in egg, milk, and vanilla.
Add flour, baking powder, and coconut.
Stir only to blend.
Divide dough in half.
Wrap half in plastic wrap. Set aside.
Roll other half on a nonstick surface (marble, parchment, silicone) to ⅜ inch thick.
Use cookie cutters to cut desired sizes of cookies.
Place on prepared cookie sheets.
Repeat with remaining dough, gathering and re-rolling scraps as necessary.
Bake for 12 to 16 minutes (depending on cookie size), or until just starting to color around the edges.
Cool slightly on cookie sheets before removing to wire cooling racks.