Combine milk and peanut butter, stirring until smooth; stir in vanilla. Add biscuit mix, stirring well.
Shape dough into 1-inch balls; roll balls in sugar, and place on ungreased cookie sheets. Make an indentation in center of each ball of dough with thumb or spoon handle.
Bake at 375° for 8 to 10 minutes or until lightly browned. Remove cookies from oven, and press a chocolate kiss in center of each cookie. Transfer cookies to wire racks to cool completely.