Position racks in the upper and lower thirds of the oven and heat to 350°F. Line 2–3 baking sheets with parchment or silicone mats.
In a medium bowl, whisk together the flour, pudding mix, baking soda, baking powder, and fine sea salt until evenly combined.
In a large mixing bowl, beat the softened butter with the brown sugar and granulated sugar on medium speed until pale and fluffy, 2 to 3 minutes, scraping the bowl as needed.
Mix in the egg, egg yolk, and vanilla until smooth and glossy.
Add the dry mixture in two additions on low speed just until no dry spots remain. Fold in the mini chocolate chips by hand to keep the dough tender.
Scoop level 2-teaspoon portions of dough, roll into balls, and place about 2 inches apart on the prepared sheets. If you like, dot a few extra chips on top for bakery-style looks.
Bake 6 to 7 minutes, swapping the pans top-to-bottom halfway through, until the edges are set and just turning light golden; the centers will look soft.
Right after baking, lightly sprinkle the cookies with flaky sea salt. Cool on the pan for 3 minutes, then transfer to a rack. Repeat with remaining dough.