Heat the olive oil in a large skillet or Dutch oven over medium heat. Add the onion, carrot, and celery and cook for 5–7 minutes, stirring occasionally, until the vegetables soften and begin to develop a sweet, savory aroma.
Add the minced garlic and cook for another minute, just until fragrant.
Stir in the vegan ground and cook for 4–5 minutes, breaking it apart with a wooden spoon. Continue cooking until it begins to brown lightly and develops a hearty texture.
Add the tomato paste, soy sauce, balsamic vinegar, oregano, basil, and smoked paprika. Stir well and cook for 1–2 minutes to deepen the flavor of the tomato paste and spices.
Pour in the crushed tomatoes and vegetable broth. Add the bay leaf, salt, black pepper, and sugar if your tomatoes are particularly acidic.
Bring the sauce to a gentle simmer, then reduce the heat to low. Cover partially and let it simmer for about 30 minutes, stirring occasionally, until the sauce becomes thick and rich.
While the Bolognese simmers, bring a large pot of generously salted water to a boil. Cook the spaghetti according to the package directions until al dente.
Reserve about ½ cup of pasta water before draining the spaghetti.
Remove the bay leaf from the Bolognese and taste the sauce. Adjust the salt, pepper, or balsamic vinegar as needed.
Add the drained pasta to the sauce and toss gently to coat. If the sauce seems too thick, add a small splash of reserved pasta water until it reaches a silky consistency.
Serve the Vegan Bolognese immediately with fresh parsley or basil, vegan Parmesan, and plenty of freshly ground black pepper.