Cream butter and sugar in a large mixing bowl; add eggs and vanilla, beating well.
Sift together flour, baking powder, and salt in a medium mixing bowl; add to creamed mixture, mixing well.
Drop dough by teaspoonfuls 3 inches apart onto greased cookie sheets; press a cherry half in center of each cookie. Bake at 375° for 8 to 10 minutes. Remove from cookie sheets, and cool on wire racks.
Oxmoor House Homestyle Recipes