Beat butter and almond butter in a large mixing bowl with an electric mixer on medium-high speed until creamy, about 30 seconds. Beat in 1/2 cup sugar, brown sugar, baking soda, cream of tartar, and salt until thoroughly combined. Beat egg, milk, and vanilla extract into moist ingredients.
Beat whole wheat flour and as much of the all-purpose flour as the mixer can handle; stir remaining flour into dough.
Combine 3 tablespoons sugar with ground almonds in a shallow bowl. Pinch off dough and roll into 1-inch balls; roll balls in almond-sugar mixture. Place cookies 2 inches apart on ungreased baking sheets.
Bake in the preheated oven until edges are firm and tops are cracked, 8 to 10 minutes. Immediately press a chocolate almond kiss into middle of each cookie; let cool.