Preheat oven to 350°. Generously brush a 10-cup nonstick Bundt pan with butter, then dust with 2 tbsp. cocoa powder; tip out excess.
In a heatproof bowl, combine chocolate chips and the remaining 1/2 cup cocoa powder. Pour 1/4 cup boiling water on top and stir until smooth. Set aside. In a second bowl, sift together flour, baking soda, baking powder, and salt; set aside.
In a large bowl with a mixer on medium speed, beat granulated and brown sugars with mayonnaise until well combined, about 1 minute. Add eggs and egg yolk one at a time, beating just until incorporated. Beat in vanilla.
With mixer on low speed, add flour mixture in three additions, alternating with chocolate mixture and beating just until blended; scrape bowl as needed.
Pour batter into prepared pan. Bake cake until a toothpick inserted into center comes out clean, 40 to 50 minutes. Let cool on a rack 15 minutes, then loosen from pan with a small spatula and turn out onto rack to cool completely.
Set cake on a platter, sift powdered sugar on top, and serve with caramel sauce.
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Make ahead: Through step 4, up to 1 day, wrapped airtight.
Note: Nutritional analysis is per serving of cake only.