In a large saucepan or Dutch oven, heat the olive oil over medium heat.
Add the chopped onion, sweet pepper, and garlic.
Cook for 5 minutes, stirring occasionally, until the vegetables have softened and become fragrant.
Stir in the chopped tomatoes and tomato paste.
Bring the mixture to a boil, then immediately reduce the heat to maintain a gentle simmer.
Cook, uncovered, for 20 minutes, allowing the flavors to meld and the sauce to thicken slightly.
Meanwhile, bring a large pot of lightly salted water to a rolling boil.
Cook the spaghetti according to package directions until al dente.
Drain the pasta well, return it to the hot pot, and cover to keep warm.
Stir the fresh basil, oregano, thyme, kosher salt, and black pepper into the tomato mixture.
Remove the pan from the heat and let it cool for a few minutes. Carefully transfer the sauce to a blender in batches (or use an immersion blender directly in the pot) and process until nearly smooth.
Return the blended sauce to the saucepan and warm it through over low heat.
Pour the sauce over the cooked pasta and toss to combine thoroughly.
Serve immediately, sprinkled generously with vegan Parmesan cheese.
Add a pinch of red pepper flakes along with the garlic for a gentle, warming heat throughout the sauce.
