How to Make It
Preheat the oven to 425°. Season the chicken with salt and pepper and dust lightly with flour. In a deep ovenproof skillet, melt 1 tablespoon of the butter in the olive oil. Add the chicken and cook over high heat, turning once, until browned on both sides, 7 minutes. Using a slotted spoon, transfer the chicken to a plate.
Meanwhile, in a food processor, pulse the 1 1/2 cups of flour with the baking powder, 1/2 teaspoon of salt and 1/4 teaspoon of pepper. Pulse in the remaining 4 tablespoons of butter until the mixture resembles coarse meal. Whisk 1/2 cup of the stock with 1/2 cup of the sour cream and drizzle over the dry ingredients; pulse until a dough forms.
Add the onion, bell pepper and garlic to the skillet and cook over high heat, stirring occasionally, until softened, 3 minutes. Return the chicken to the skillet. Stir in the paprika and caraway and cook for 30 seconds. Add the remaining 2 cups of chicken stock and 1/2 cup of sour cream and stir until smooth. Add the thyme and bring to a boil.
Scoop twelve 3-tablespoon-size mounds of biscuit dough over the chicken. Transfer the skillet to the oven and bake for about 20 minutes, until the sauce is bubbling and the biscuits are cooked. Turn on the broiler and broil for about 2 minutes, until the biscuits are golden. Serve the goulash in bowls, spooning the biscuits on top.