Preheat oven to 325°F (163°C). Line baking sheets with parchment paper.
In a mixing bowl, beat together the melted and cooled browned butter, salt, and peanut butter until smooth.
Add sugars and beat until creamy, then beat in eggs and vanilla until just combined.
Whisk together flour, baking soda, and spice (if using). Stir into peanut butter mixture until incorporated. Dough should be soft and scoopable. If it feels too stiff, you can add the tiny splash of milk.
Scoop rounded teaspoonfuls (or use a small cookie scoop) onto baking sheets. Flatten slightly with a fork in a criss-cross pattern.
Bake 11–13 minutes, until edges are set and centers are still soft. For chewier cookies, pull early; for crispier edges, bake toward 13 minutes.
Cool on sheets 5 minutes, then transfer to a wire rack.
Notes
For gluten-free cookies, use 140 grams of gluten-free all-purpose blend such as Cup4Cup.