Preheat oven to 350°F and line a baking sheet with parchment paper.
Cream butter, peanut butter, and sugars in a large mixing bowl until smooth and creamy.
Add egg, sourdough discard, and vanilla extract. Mix until fully combined.
In a separate bowl, whisk together flour, baking soda, and salt.
Gradually mix dry ingredients into wet ingredients until just combined.
Shape dough into 1 tablespoon-sized balls and place on prepared baking sheet.
Flatten each cookie with a fork in a crisscross pattern.
Bake for 10–12 minutes, until edges are lightly golden.
Allow cookies to cool on the baking sheet for 5 minutes, then transfer to a wire rack.