Preheat the oven to 350°F and line or grease two half-sheet pans. (You will do more batches than this, but two will get you started.)
Mix together the melted butter, sugar, brown sugar, eggs, vanilla, and salt. Add the jar of peanut butter and mix until fully combined. Do not overmix. Scrape the bowl to ensure that everything is fully incorporated.
Add the baking soda and flour and mix just until combined. Stir in the chocolate chips, if using.
Use a tablespoon or cookie scoop to scoop and roll the cookie dough into balls. If you like, you can roll the balls in sugar.
Place the peanut butter cookie dough balls on a cookie sheet, leaving about 1 to 1/2″ of space between each. Score each cookie with the tines of a fork, pressing the cookies down slightly and making a crisscross pattern. (You can also use cookie stamps like these, though the cookies do spread a bit so you’ll lose some of the effect.)
Bake for 11 to 12 minutes, until the bottoms are light golden brown and the tops look dry.
Let cool for a couple minutes on the pan, then transfer to a cooling rack. Repeat with the remaining cookie dough. Serve with a big glass of cold milk.
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