How to Make It
Place 1⁄2 cup of the butter in freezer until solid, at least 30 minutes.
Preheat oven to 350°F. Heat a medium skillet over medium. Add caraway seeds, and cook, stirring constantly, until lightly toasted, about 1 minute. Remove seeds from skillet, and set aside.
Add oil to skillet, and heat over medium-high. Add onion, and cook, stirring often, until starting to soften, about 3 minutes. Reduce heat to medium-low, and cook, stirring occasionally, until tender and browned, about 15 minutes. Season with 1⁄4 teaspoon of the salt. Remove onions from skillet, and let cool 10 minutes.
Place a 9-inch cast-iron skillet in preheated oven. Stir together flours, baking powder, baking soda, 1⁄2 teaspoon of the salt, and toasted caraway seeds in a medium bowl. Whisk together cream, egg, and honey in a separate bowl.
Remove butter from freezer. Using the large holes on a box grater, grate frozen butter into coarse shreds. Add shredded butter to flour mixture, stirring to combine. Add cream mixture, cheese, and caramelized onions to flour mixture; stir just until dough comes together. Turn dough out onto a lightly floured surface; pat into an 8-inch circle. Add remaining 2 tablespoons butter to hot cast-iron skillet, swirling to melt. Gently place dough in skillet; sprinkle with remaining 1⁄4 teaspoon salt.
Bake bread in preheated oven until sides and top are golden brown, 20 to 25 minutes. Remove from oven, and let cool in skillet 5 minutes. Remove bread from skillet, and place on a wire rack to cool to room temperature, about 30 minutes. Sprinkle with thyme, if desired; serve with Whipped Sweet Potato Butter.