In a large skillet or pot (I used a Dutch oven), heat cooking oil over medium to medium-high heat. Sauté onion for 2 minutes, add garlic and cook until onions are soft.
Add all veggies, except tomatoes, and cook, covered, for 5 minutes. Stir occasionally.
Add thyme, oregano, paprika powder, salt, and pepper. Stir well to combine.
Shove half of the veggies to one side, layer with half of the pasta noodle pieces. Cover with the remaining veggies and another pasta layer. Finish with tomatoes and add water or vegetable stock.
Cover and cook for 20-25 minutes. Stir gently every 5 minutes. Last 5 minutes, add cheese on top and recover.