Heat olive oil in a large skillet over medium heat.
Add diced onion and minced garlic to the skillet and sauté for 3-4 minutes until softened.
Add ground beef to the skillet and cook, breaking it apart with a spoon, until browned and cooked through, about 6-8 minutes.
Drain any excess fat from the skillet.
Add diced green and red bell peppers and sliced mushrooms to the skillet. Cook for 5 minutes until vegetables are tender.
Stir in the diced tomatoes with their juice, tomato sauce, dried oregano, dried basil, smoked paprika, black pepper, and salt.
Reduce heat to low and simmer the mixture for 7-10 minutes, stirring occasionally, to allow flavors to meld.
While the beef mixture simmers, prepare the cooked white rice according to package instructions if not already prepared.
Serve the ground beef mixture hot over cooked white rice.