Preheat the oven to 190°C (375°F).
In a large oven-safe pot or Dutch oven, heat the olive oil over medium heat.
Add the chopped onion and minced garlic to the pot and sauté for 3-4 minutes until softened and fragrant.
Add the diced red bell pepper, yellow bell pepper, and zucchini to the pot. Cook for 5 minutes, stirring occasionally.
Add the canned diced tomatoes, vegetable broth, dried oregano, dried basil, salt, and black pepper to the pot. Stir to combine.
Add the penne pasta and chopped spinach to the pot. Stir well to ensure the pasta is submerged in the liquid.
Bring the mixture to a gentle boil, then remove from heat.
Sprinkle the shredded mozzarella cheese evenly over the top of the pasta mixture.
Sprinkle the grated Parmesan cheese over the mozzarella.
Cover the pot with a lid or aluminum foil and place it in the preheated oven.
Bake for 25 minutes, then remove the lid or foil and bake for an additional 10 minutes until the cheese is golden and bubbly.
Remove the pot from the oven and let it cool for 5 minutes before serving.