1. Make the buns: Preheat the oven to 400°. Lightly grease 2 cast iron straight-sided muffin pans (6 cups each) with nonstick cooking spray. Stir together the cornbread mix, flour, milk, sour cream, and 1 egg in a large bowl until well blended. Stir in the chives, crumbled bacon, and cheese. Fill each of the wells in the prepared muffin pans three-quarters full. Bake until golden brown, 10 to 12 minutes. (Any remaining batter can be made into additional muffins.)
2. Make the chipotle mayo: Combine the mayonnaise, chipotle, and adobo sauce in a small bowl until well blended. Set aside.
3. Make the burgers: Melt the butter in a 12-inch cast iron skillet over medium-low heat. Add the onion rings and cook, stirring occasionally, until softened, 8 to 10 minutes. Remove from the skillet; wipe the skillet clean.
4. Combine the ground chuck, egg, breadcrumbs, garlic, salt, and pepper in a large bowl. Blend well. Divide into 12 equal portions. Pat out into thin burgers. Heat the skillet over medium to medium-high heat until hot. Cook the burgers, in batches, to desired degree of doneness. Top each burger with a slice of cheese.
5. To serve, slice the cornbread muffins to make buns. Spread a thin layer of the Chipotle Mayo on the tops and bottoms. Place a burger on each bottom half.Top with onion rings. Place the tops on the burgers and serve.