Heat oven to 375 degrees Fahrenheit. Cream together shortening, peanut butter, brown sugar, and 1/2 cup sugar. Add egg, milk, and vanilla. Beat well.
Stir together flour, baking soda, and salt. Add to creamed mixture. Beat on low speed until stiff dough forms. Shape into 1-inch balls. Roll in sugar. Place 2 inches apart on an ungreased cookie sheet.
Bake 10 to 12 minutes or until golden brown. Top each cookie immediately with an unwrapped chocolate piece, pressing down firmly so that cookie cracks around the edge. Remove from the cookie sheets to cool.