Season the beef steaks with salt and pepper. Dredge in flour, shaking off excess.
In a large sauté pan, heat oil and 1 tablespoon of butter over medium-high heat. Cook the beef steaks until golden brown on both sides, about 2-3 minutes per side. Remove and set aside.
In the same pan, add the remaining butter. Sauté the onion, garlic, and carrots until softened, about 5 minutes.
Add tomato paste to the pan, stirring to combine. Cook for 1-2 minutes before adding beef broth, bay leaf, and allspice. Simmer until the sauce thickens, about 10 minutes.
Return the beef steaks to the pan, spooning the sauce over them. Cook for an additional 10 minutes to heat through.
Garnish with fresh parsley and serve immediately.
