Preheat oven to 350º.
Cream 1/2 cup butter and 3/4 cup brown sugar. Add 3 tablespoons granulated sugar until fully combined, about 30 seconds. Beat in 1 egg, 1/2 teaspoon vanilla, and 2 tablespoons milk.
In a separate medium size bowl, combine 1 1/2 cups flour, 2 tablespoons corn starch, 1 teaspoon baking soda, and a pinch of salt . Stir with a fork until combined.
Add flour mixture to wet ingredients, a little at a time, until fully combined.
Mix in 1/2 cup peanut butter.
Using a small ice cream scooper, scoop dough onto a cookie sheet lined with parchment paper. Using your hands, form each scoop into a ball.
Refrigerate the dough for 1 hour.
Bake 10-12 minutes. Let the cookies cool for 1 minute. Using the back of a teaspoon or your thumb, create an indentation in the middle of the cookie. Fill the indentation with about 1 teaspoon of jelly.