Heat olive oil in a large skillet over medium heat.
Add diced onion, carrot, and celery to the skillet and sauté for 5 minutes until softened.
Add minced garlic and sliced mushrooms, cook for another 3 minutes until mushrooms release their moisture.
Add ground beef to the skillet and cook, breaking it apart with a spatula, until browned and cooked through, about 7 minutes.
Drain excess fat from the skillet if necessary.
Stir in tomato paste and cook for 1 minute to deepen the flavor.
Add diced tomatoes with their juice, beef broth, dried oregano, dried basil, salt, black pepper, and crushed red pepper flakes. Stir to combine.
Bring the mixture to a simmer, reduce heat to low, and cook uncovered for 15 minutes, stirring occasionally.
Stir in frozen peas and cook for an additional 3 minutes until peas are heated through.
Remove from heat and stir in chopped fresh parsley.
Serve warm as a hearty, cozy dinner.