In a large pot or deep skillet, heat olive oil over medium heat.
Add the chopped onion and sauté for 3-4 minutes until translucent.
Add the minced garlic and cook for 1 minute until fragrant.
Pour in the vegetable broth, diced tomatoes with their juice, dried oregano, dried basil, salt, and black pepper.
Add the dry penne pasta to the pot and stir to combine all ingredients.
Bring the mixture to a boil over high heat.
Reduce heat to medium-low and simmer uncovered, stirring occasionally, for 12-15 minutes or until the pasta is cooked al dente and most of the liquid is absorbed.
Five minutes before the pasta is done, stir in the chopped fresh spinach and cook until wilted.
Remove the pot from heat and stir in the grated Parmesan cheese until melted and combined.
Serve immediately, garnished with extra Parmesan if desired.