In a large mixing bowl, combine the melted butter, brown sugar, peanut butter, milk, vanilla, and egg. Whisk or beat until smooth and fully combined.

In a separate bowl, whisk together the flour, salt, and baking soda. Add the dry mixture to the wet ingredients and stir until a soft dough forms. (If the dough feels sticky, chill it for 10–20 minutes.)

Preheat oven to 350°F (175°C) and line a baking sheet with parchment paper.

Scoop about 1 tablespoon of dough per cookie. Roll each piece into a ball, then roll the ball in granulated sugar to coat.

Place cookie balls onto the baking sheet. Use a fork to gently press a criss-cross pattern on the top of each ball.

Bake for 9–11 minutes, or until the edges are just set. The centers should look slightly soft — they firm up as they cool.

Allow cookies to cool on the baking sheet for 5 minutes, then transfer to a wire rack.