Preheat oven to 375°F. Line a baking sheet with parchment paper, aluminum foil, or a silicone baking mat and set aside.
In the bowl of a stand mixer (or a large mixing bowl), beat 8 tablespoons unsalted butter (room temperature) with ¾ cup brown sugar and ¼ cup granulated sugar until the mixture is light and fluffy, about 2–3 minutes; scrape down the bowl as needed.
In a separate medium bowl, whisk together 1 cup all-purpose flour, 3 oz. unsweetened cocoa powder (¼ cup + 1 Tbsp), ½ teaspoon baking soda, ¼ teaspoon salt, and ¾ teaspoon ground red pepper until evenly combined.
Add 1 egg, 1 egg yolk, and 1 teaspoon vanilla extract to the creamed butter-sugar mixture and beat just until combined.
Add the dry ingredients to the wet ingredients and gently fold or mix on low speed until just combined. Do not overmix.
Scoop portions of dough onto the prepared baking sheet, spacing each cookie about 2 inches apart.
Bake in the preheated oven for 8–9 minutes, until the edges are set (centers may still look slightly soft).
Remove the baking sheet from the oven and let the cookies cool on the sheet for 2 minutes, then transfer the cookies to a cooling rack to cool completely.