Pulse carrots, onion, garlic, and sun-dried tomatoes in food processor until fully shredded.
Add olive oil to large, deep skillet or pan and heat to medium heat. Add shredded veggie mixture and cook 2-3 minutes until fragrant and most of the liquid has cooked off.
Grind walnuts in the food processor until they are a consistent, coarse meal.
Add walnuts to the skillet along with veggie mixture. Cook 1-2 minutes until fragrant.
Puree fire roasted tomatoes in food processor and add to the skillet along with all other remaining ingredients. Bring to a simmer and cook 15-12 minutes or until desired consistency is reached.
While the Bolognese is cooking, prepare noodles according to package instructions.
Serve Bolognese over a bed of veggie spaghetti noodles and garnish with basil (optional).