Combine the fennel stems and fronds along with the anchovy, garlic, mustard, lemon, zest, avocado oil, and parmesan, if using in a food processor or other blender. Pulse until well chopped and then blend until smooth pesto forms. Season to taste with salt and pepper and set aside.
Heat a large pan over medium high heat. When hot, add a tablespoon of oil and then add the meatballs. Cook until browned on all sides and cooked through, about 10 minutes. Remove the meatballs to a serving bowl and set aside. Do not clean the pan.
Add the sliced fennel bulb to the uncleaned pan and sauté until lightly browned and softened, about 10 minutes.
While the fennel cooks, roast the tomatoes - line a foil rimmed baking sheet with aluminum and toss the tomatoes with a couple of teaspoons of avocado oil and season with salt and pepper. Broil on high until charred in spots, about 10 minutes. Remove from oven and cool.
Add the noodles to the softened fennel and cook for another 5 minutes to remove any excess water. Turn off the heat and remove the pan from the burner. Add the pesto, meatballs, and charred tomatoes and toss to combine. Serve with additional parmesan, if desired.