Arrange 2 racks to divide the oven into thirds and heat the oven to 350℉. Lined 2 rimmed baking sheets with parchment paper or silicone baking mats.

Place 1 cup smooth peanut butter, ¾ cup granulated sugar, and 1 large egg in a large bowl. Mix with a flexible spatula until well-combined.

Scoop the dough out into 24 (level 1-tablespoon) portions. Roll into balls. Place the dough balls at least 2 inches apart on the baking sheets, 12 per sheet. Flatten each dough ball with a fork until about 2 inches wide and ¼-inch thick, creating a crosshatch pattern.

Bake for 5 minutes. Rotate the baking sheets between racks and from front to back. Bake until the centers are set, the cookies are lightly puffed, and the edges are firm, 5 to 7 minutes more. Let cool completely on the baking sheets, about 30 minutes. The cookies will firm up as they cool.