Make the cookie dough. In a medium bowl, whisk together the brown sugar and eggs until combined. Add the peanut butter and whisk until combined. Cover the bowl with plastic wrap and refrigerate for 1 hour.
After 1 hour, remove the chilled dough from the refrigerator. Use a 3-tablespoon cookie dough scoop to portion the cookie dough into balls, placing them in tight rows on a sheet pan. Cover loosely with plastic wrap and freeze for at least 15 minutes.
Prepare your oven and pans. While the cookies are in the freezer, prepare your oven. Position a rack in the center of the oven and preheat the oven to 350°F. Line two half sheet pans with parchment paper.
After 15 minutes, remove the frozen dough from the freezer. Place them at least 3 inches apart on the prepared sheet pans.
Bake the cookies. Bake one pan at a time (keeping the other in the refrigerator) for 16 minutes, until the edges have set but the centers are still gooey. Cool the cookies on the pan on a wire rack for 20 minutes, or until the edges and bottoms of the cookies feel firm to the touch. Repeat with remaining cookie dough balls.
Serve and store. Serve warm or at room temperature. The cookies can be stored, in an airtight container at room temperature, for up to 3 days.