Preheat oven to 350° and prepare baking sheets with silicone mats or parchment paper.
In a small bowl, mix the flour*, baking soda, and salt. Whisk together until well combined. Set aside.
In a large mixing bowl, add butter and granulated sugar. Beat on medium-high for about 2 minutes (mixture will be light in color and lumpy but sugar should be completely incorporated).
Add peanut butter**, egg, vanilla extract, and milk. Beat on medium for 30 seconds to 1 minute until the butter lumps dissolve and the mixture is smooth and thick.
Slowly add dry ingredients (about ¼-⅓ cup at a time) beating on low until combined after each addition.
Using a cookie scoop, drop cookie dough balls onto the prepared baking sheet. Make sure they are at least 3" apart to account for spreading.
Using a fork, create a cross-hatch pattern on each cookie, flattening slightly. Sprinkle the top of each cookie with granulated sugar. Bake for 9-11 minutes.
Remove from oven and let cool on the cookie sheet for a least 5 minutes before moving to prevent cookies from baking. Serve warm or let cool completly on wire rack.