Preheat the oven to 350°F. Line two baking sheets with parchment paper and set aside.
Put the rolled oats in a blender or food processor and pulse until they form a fine to medium oat flour—stop before they become gummy. Transfer to a medium bowl.
Whisk the all-purpose flour, oat flour, salt, baking powder, baking soda, and instant espresso powder together in the bowl until evenly distributed; set aside.
In a stand mixer fitted with the paddle (or using a hand mixer), cream the butter with the granulated and brown sugars on medium speed until the mixture is pale and fluffy, about 3–4 minutes.
Add the eggs one at a time, mixing until incorporated, then add the vanilla and beat for 20–30 seconds more, scraping the bowl down once.
With the mixer on low, add the dry ingredient mixture in two additions, mixing just until no dry streaks remain. Avoid overmixing to keep the cookies tender.
Using a spatula, fold in the chocolate chips, grated chocolate, and the chopped nuts until evenly distributed through the dough.
Scoop the dough into rounded 2-tablespoon portions onto a baking sheet, spacing them about 2½ inches apart. For thicker cookies, cover the sheet and chill the scooped dough in the refrigerator for 30–45 minutes (this step is optional but recommended).
Bake one sheet at a time in the preheated oven for 12–14 minutes, rotating the pan halfway through. Cookies are done when edges are golden and centers still look slightly soft.
Allow the cookies to rest on the baking sheet for 5–6 minutes so they set, then transfer to a wire rack to cool completely.