Preheat the oven to 325°F.
Pat the cube steaks dry and season both sides with salt and black pepper. Dredge lightly in flour, shaking off the excess.
Heat olive oil in a large Dutch oven over medium-high heat. Sear the cube steaks for 2–3 minutes per side until browned. Work in batches if needed. Transfer steaks to a plate.
Lower the heat to medium. Add the sliced onion and sauté for 5 minutes until softened.
Stir in the grated carrots and cook for 2 minutes until they begin to soften.
Add the garlic and cook until fragrant.
Stir in the tomato paste, stir it, and pour in the crushed tomatoes and beef broth. Stir in thyme and paprika. Bring to a gentle simmer.
Return the cube steaks to the Dutch oven, add them into the sauce. Spoon a bit of sauce over the top.
Cover with the lid and transfer to the oven. Bake for 2 to 2 ½ hours, or until the steaks are fork-tender.
Taste, adjust seasoning if needed, and serve warm.