Heat olive oil in a large skillet over medium-high heat for one minute. Add ground beef and cook until browned, breaking it into small pieces as it cooks, approximately 8-10 minutes. Drain excess fat if needed, then set the beef aside on a clean plate.
In the same skillet, add diced onion and sauté until softened and golden, about 4-5 minutes. Add minced garlic and cook for another 30 seconds until fragrant. Stir in tomato paste and cook for 1-2 minutes to caramelize slightly.
Return the cooked ground beef to the skillet and add diced potatoes and sliced carrots. Stir well to coat everything with the flavorful base. Pour in beef broth and bring the mixture to a simmer over medium heat.
Add dried thyme, oregano, paprika, salt, and black pepper, then stir in diced tomatoes. Reduce heat to medium-low and let the cozy ground beef skillet recipe simmer uncovered for 20-25 minutes, stirring occasionally, until potatoes are fork-tender.
Add green beans during the final 5 minutes of cooking time. Taste and adjust seasoning as needed. The skillet should be slightly thick and hearty without being completely dry; add a splash more broth if needed.