Prep the oven and pans. Heat the oven to 350°F (175°C). Line two baking sheets with parchment paper or silicone mats.
Cream the fats and sugars. In a large bowl, beat the butter, peanut butter, brown sugar, and granulated sugar on medium speed for 2–3 minutes until light and creamy. Scrape the bowl.
Add wet ingredients. Mix in the egg and vanilla until smooth and slightly fluffy, about 30 seconds.
Combine dry ingredients. In a separate bowl, whisk flour, baking soda, baking powder, salt, and cornstarch.
Bring the dough together. Add the dry ingredients to the wet in two additions, mixing on low just until combined.
Do not overmix.
Fold in the chips. Stir in semisweet and milk chocolate chips until evenly distributed.
Chill (optional but helpful). For thicker cookies, chill the dough 20–30 minutes. If you’re short on time, you can bake right away; they’ll just spread a touch more.
Scoop and shape. Use a 2-tablespoon scoop (about 35–40 g) to portion dough. Roll into balls and space 2 inches apart on prepared sheets.
Bake. Bake 9–11 minutes, until the edges are set and lightly golden but centers look slightly underdone.
This underbake is key for chewiness.
Finish and cool. Immediately sprinkle with a pinch of flaky sea salt. Let cookies cool on the sheet for 5 minutes, then transfer to a rack to cool completely.