Preheat oven to 375 degrees F (190 degrees C).
Beat peanut butter and shortening together in a bowl using an electric mixer until smooth and creamy; add white sugar and brown sugar and beat until fluffy. Add egg, milk, and vanilla extract to creamed mixture and beat until smooth.
Mix flour, baking soda, and salt together in a separate bowl; gradually beat into the creamed mixture until dough is just mixed. Shape dough into 1-inch balls and arrange on a baking sheet.
Bake in the preheated oven until cookies are lightly browned, 8 to 10 minutes. Immediately press a chocolate kiss into the center of each cookie. Transfer cookies to a wire rack to cool.
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