Preheat your oven to 350°F. Grease an 8x8 baking dish.
In a large sauté pan over medium heat, melt the 185 grams butter. Add the 1 tablespoon Szechuan peppercorns and 1 cinnamon stick. Let the butter foam and then subside, cooking until you see browned bits at the bottom of the pan, about 5 minutes. Take the pan off the heat. You can strain the butter to remove the peppercorns and cinnamon stick, then return just the infused butter to the pan.
While the butter is infusing, melt the 1 ounce unsweetened chocolate and 1/3 cup semisweet chocolate chips together in a double boiler or microwave. Stir in the 1 tablespoon espresso until combined.
Stir the 3/4 cup brown sugar, 1/2 cup granulated sugar, 1 tablespoon milk, 2 teaspoons vanilla extract, and 1/4 teaspoon kosher salt into the warm, infused butter in the pan. Then, stir in the 3/4 cup cocoa powder and the melted chocolate-espresso mixture. Beat in the 3 eggs one at a time, ensuring each is fully incorporated. Finally, stir in the 3 cups flour until just combined, being careful not to overmix.