Preheat oven to 375°F. Line a baking sheet with parchment paper. Beat shortening and peanut butter with a stand mixer fitted with a paddle attachment on medium speed until smooth, about 1 minute. Gradually add brown sugar and 1/2 cup of the granulated sugar, beating until light and fluffy, about 2 minutes. Add egg, milk, and vanilla; beat on medium-high speed until fully combined and fluffy, about 1 minute. Stir together flour, baking soda, and salt in a bowl; add to shortening mixture, beating on low speed until fully combined, about 1 minute.

Roll dough into 36 (1-inch) balls. Place remaining 1/4 cup granulated sugar in a bowl; roll balls in sugar to coat.

Arrange 12 of the dough balls on prepared baking sheet spaced 2 inches apart. Bake in preheated oven 8 minutes. Remove from oven; immediately press 1 chocolate kiss into center of each cookie. Return to oven; bake at 375°F until lightly browned, about 2 minutes. Remove from oven; cool on baking sheet 3 minutes. Transfer cookies to a wire rack. Repeat process 2 times with remaining 24 balls and chocolate kisses. Let cookies cool completely on wire rack, about 20 minutes.