Arrange 2 oven racks to divide the oven into thirds and preheat the oven to 350°F (175°C). Line 2 rimmed baking sheets with parchment paper or silicone baking mats.
In a large mixing bowl, combine the peanut butter, granulated sugar, and egg. Mix with a flexible spatula until smooth and fully combined.
Scoop the dough into 24 level tablespoon-sized portions. Roll each portion into a ball.
Place the dough balls at least 2 inches apart on the prepared baking sheets, about 12 cookies per sheet.
Flatten each cookie with a fork to create a classic crosshatch pattern. Press until each cookie is about 2 inches wide and 1/4-inch thick.
Bake for 5 minutes. Rotate the baking sheets between racks and turn them from front to back.
Continue baking for another 5 to 7 minutes, or until the centers are set, the cookies are lightly puffed, and the edges feel firm.
Let the cookies cool completely on the baking sheets for about 30 minutes. The 3 Ingredient Peanut Butter Cookies Recipe becomes firmer as the cookies cool.