Preheat your oven to 190°C (375°F) and lightly oil a 9x13 inch baking dish.
Bring a large pot of salted water to a boil, then cook the pasta until just al dente, about 1 minute less than package instructions. Drain and set aside.
While the pasta cooks, chop your vegetables into bite-sized pieces. Heat olive oil in a sauté pan over medium heat, then add the vegetables. Sauté for about 8 minutes until they soften and develop some caramelized edges, filling your kitchen with a fragrant aroma.
In a mixing bowl, combine the drained tomatoes, nutritional yeast, minced garlic, smoked paprika, salt, and pepper. Use a spoon to mash the tomatoes slightly, creating a chunky sauce with rich flavor.
Add the cooked pasta and sautéed vegetables to the bowl with the tomato sauce. Toss everything together until well coated and evenly mixed.
Transfer the pasta mixture into your prepared baking dish, spreading it out evenly. In a small bowl, stir the vegan cheese with plant-based milk until creamy, then dollop this mixture over the top of the pasta.
Bake uncovered in the oven for 20-25 minutes until bubbling and the top is golden brown. Keep an eye on it towards the end to prevent burning.
Remove the bake from the oven and let it rest for about 5-10 minutes. This helps it set and makes serving easier, with a slightly crisp top and tender inside.
Slice into portions and serve hot, garnished with fresh herbs if desired. Enjoy the comforting, cheesy aroma and hearty texture of this vegan pasta bake!