Sift together flour, cocoa powder, baking powder, baking soda, and salt into a large bowl. In another bowl, whisk together sugar, buttermilk, butter, and eggs until thoroughly combined. Stir buttermilk mixture into flour mixture just until a smooth dough forms.
On a lightly floured work surface, pat dough flat and lightly flour. Roll out dough to a 1/3-inch thickness. Cut into rounds with a 2 1/2-inch cookie cutter (to lift rounds from work surface, use a thin spatula). Reroll and cut scraps.
Place a caramel in the center of each round, pinch dough closed around it, and gently roll into a smooth ball.
Line a baking sheet with paper towels. Fill a wide shallow bowl with 1 inch sugar. In a large heavy pot, heat 4 inches oil until it registers 350 degrees on a candy thermometer. In batches of 4, fry doughnuts 5 minutes, turning once with a slotted spoon and adjusting heat as needed. Transfer doughnuts to prepared sheet; let rest 4 minutes. Roll in sugar to coat. Serve immediately.