Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper.
In a large mixing bowl, combine the peanut butter, granulated sugar, egg, baking soda, vanilla extract, and salt. Stir until the mixture is smooth and well combined.
Roll the dough into 1-inch balls and place them about 2 inches apart on the prepared baking sheets.
Flatten each ball slightly with the back of a fork, creating a crisscross pattern.
Sprinkle the tops of the cookies evenly with the red and green Christmas sprinkles, gently pressing them into the dough so they stick.
Bake in the preheated oven for 10 to 12 minutes, or until the edges are lightly golden but the centers remain soft.
Remove the cookies from the oven and allow them to cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.