Heat olive oil in a large skillet over medium heat.
Add diced onion and cook for 3-4 minutes until softened.
Add minced garlic and cook for 1 minute until fragrant.
Add ground beef to the skillet, breaking it apart with a spoon. Cook until browned and no longer pink, about 6-8 minutes. Drain excess fat if necessary.
Add diced red and green bell peppers and diced carrots to the skillet. Cook for 5 minutes until vegetables begin to soften.
Stir in smoked paprika, dried oregano, dried thyme, crushed red pepper flakes, salt, and black pepper.
Add canned diced tomatoes and beef broth. Stir to combine.
Reduce heat to medium-low, cover the skillet, and simmer for 10 minutes until vegetables are tender and flavors meld.
Uncover and stir in chopped fresh spinach. Cook for an additional 2 minutes until spinach wilts.
Adjust seasoning with salt and black pepper if needed.
Serve hot as a hearty, pasta-free ground beef dinner.