Weigh or lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking soda, and salt, stirring with a whisk; set aside.
Place brown sugar, peanut butter, and oil in the bowl of a stand mixer. Cream together with paddle attachment until fully incorporated (about 1 minute). Add milk, vanilla, and egg; mix on medium-low speed another 1 minute or until emulsified. Add flour mixture, and mix on low speed until just combined (about 15 seconds). Using a rubber spatula, make sure there are no rogue streaks of peanut butter.
Scoop dough with a 1-tablespoon cookie scoop 2 inches apart onto baking sheets lined with parchment paper (or roll tablespoonfuls of dough into balls and arrange on baking sheets). Bake at 350°F for 10 minutes. Remove from oven; immediately make a “thumbprint” impression with the handle of a wooden spoon (tamp down 2 or 3 times for a nickel-sized indentation). Place cookies on a wire rack; cool completely. Spoon 1/2 teaspoon jelly into indentation of each cookie.
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