Preheat your oven to 375°F (190°C) and line a baking sheet with parchment paper.
Using a stand mixer fitted with the paddle attachment (Speed 4), beat the softened butter alone until smooth and creamy. Add both sugars and continue beating for 2–3 minutes, until light and fluffy. Add the peanut butter and mix until fully incorporated. Finally, add the egg and beat again until well combined.
In a separate mixing bowl, whisk together the flour, baking soda, baking powder, and salt.
Gradually add the dry ingredients to the wet mixture on low speed (Speed 1–2) until just combined. Stop mixing as soon as no dry flour remains. Overmixing can cause the cookies to turn out more cakey instead of tender.
Scoop dough using a 1.5 tbsp cookie scoop, leveling it lightly. Roll each portion in turbinado sugar until generously coated. Avoid overfilling the scoop, as oversized dough balls may not flatten completely.
Place the dough balls on the baking sheet, spacing them about 2 inches apart. Flatten each ball slightly with the bottom of a glass or a fork, applying gentle pressure.
Bake for 7–10 minutes, until the edges are set and the centers still look slightly soft and puffy. In many ovens, about 9 minutes yields the best texture.
Let the cookies cool on the baking sheet for 10–15 minutes until they have set enough to handle. They will continue to firm up as they cool.