Beat shortening, 1/2 cup white sugar, brown sugar, peanut butter, egg, milk, and vanilla extract together in a large bowl with an electric mixer until creamy.
Whisk flour, baking powder, and salt together in a bowl. Stir flour mixture into peanut butter mixture.
Pour 1/4 cup white sugar into a shallow bowl. Wrap each chocolate kiss in about 1 1/2 teaspoons of dough and shape into a ball. Roll the dough ball in sugar to coat. Place each ball about 1 1/2 inches apart on baking sheets.
Bake cookies in the preheated oven until chocolate softens and cookie is set, about 6 minutes. Flatten cookies immediately by pressing on them with the bottom of a glass.
You can substitute 1/2 teaspoon vanilla extract and 1/2 teaspoon almond extract for the 1 teaspoon vanilla extract.
You can try several variations: mix mini chocolate chips into the dough before forming the dough into balls; flatten the dough balls with a sugar-coated glass bottom before baking and press a few candy-coated chocolate pieces in the top; bake the cookies without kisses and press the kisses into the cookie immediately after baking.