Preheat oven to 350°F (175°C) and line two baking sheets with parchment. Whisk together flour, baking soda, and salt in a medium bowl.

Cream butter, peanut butter, brown sugar, and granulated sugar in a large bowl until light and fluffy, about 2 minutes.

Beat in egg, vanilla, and sourdough discard just until combined, about 30 seconds.

Add flour mixture all at once, mixing on low until no dry streaks remain, about 20 seconds.

Scoop tablespoon‑sized balls onto sheets, press with a fork in a crosshatch, and bake 10 to 12 minutes until edges are set and lightly golden. Cool on the sheet 5 minutes, then transfer to a wire rack. Sprinkle with flaky salt if desired.