Preheat oven to 375 degrees F. Line baking sheets with a silicone mat or parchment paper, then set aside.
In a medium mixing bowl, stir together 1 ¾ cup all-purpose flour, ¾ teaspoon baking soda, and ¾ teaspoon salt. Set aside.
In the bowl of a stand mixer (or a large mixing bowl using a hand mixer), beat together ¾ cup creamy peanut butter and ½ cup unsalted butter until smooth. Scrape the sides of the bowl.
Add ¾ cup brown sugar and ½ cup granulated sugar to the peanut butter and beat until combined. Add 1 large egg, 1 ½ teaspoons vanilla extract, and 3 tablespoons 2% milk and mix until smooth. Scrape the sides of the bowl.
Add the dry ingredients to the wet ingredients in two additions, mixing until just combined after each addition.
Divide the cookie dough balls using a 1-tablespoon measuring spoon. Roll each portion of dough into a 1-inch ball and place it on the prepared baking sheets 2 inches apart from each other. (The cookies will spread during baking.)
Using a fork, gently press down on the dough ball with the tines until the cookie is halfway flattened. Turn the fork 90 degrees and press down again to make a criss-cross pattern in the dough. Repeat with remaining dough.
Bake cookies for 7 to 8 minutes or until set. Carefully remove from the oven and cool on the pans for 5 minutes. Transfer to a wire rack to cool completely.