Heat the oil over medium in a large stockpot, then add onion, carrots, celery and basil.
Season with salt and pepper and cook, stirring frequently, until onions are transparent and fragrant, about three minutes.
Add pancetta and stir, cooking for about another three minutes.
Add tomato paste and white wine and stir to combine, then allow to cook until wine is evaporated.
Add beef and cook, stirring frequently, until slightly brown, about eight minutes.
Add bay leaves and beef stock and bring to a boil.
Reduce so liquid is simmering and set timer for 1.5 hours, stirring every once in a while, until liquid is completely absorbed.
Add Earth Balance and oat milk and stir until Earth Balance is melted.
Allow to simmer until oat milk is absorbed.
Remove bay leaves and lower temperature to low until pasta is done cooking.
When there are about 30 minutes left on the timer, cook the gluten-free tagliatelle per the package instructions, reserving ½ cup pasta cooking water.
Scoop beef mixture into a food-safe, large, shallow pasta bowl, then add the pasta cooking water.
Drain pasta and add directly to the bowl, then toss to combine.