Heat the oil over medium-high heat in a large skillet, then add the veggies (garlic, onion, carrot, and celery) and cook over medium-high heat until golden brown, stirring occasionally.
Add the vegan ground beef and cook until golden brown, stirring occasionally.
Add the wine and cook until the liquid is absorbed.
Stir in all the remaining ingredients (except the pasta and milk), stir, and bring to a boil. Then simmer for at least 30 minutes.
Meanwhile, cook the spaghetti according to package directions. Drain and set aside.
Remove the bay leaf, add the milk, and stir until combined.
Toss pasta with sauce adding pasta water to thin out if needed.
Serve immediately with vegan Parmesan cheese. Store leftovers in an airtight container in the refrigerator for up to 1 week or in the freezer for up to 3 months.