Bring a large pot of water to a boil and cook the gluten-free fettuccine until just tender to the bite, then drain.
Heat a large skillet and add some water, broth, or oil. Sauté the minced garlic and chopped sun-dried tomatoes for about 2 minutes, adding water gradually if it gets too dry.
Stir in the Italian seasoning, balsamic vinegar, and tomato paste; cook for an additional 2 to 3 minutes until the mixture becomes fragrant and slightly caramelized.
Add the cherry tomatoes along with a splash of water to the skillet, cover it, and let cook for 3 to 4 minutes until the tomatoes soften. Then, gently smash the tomatoes with your spoon to break them down.
Pour in the thick coconut milk and sprinkle the nutritional yeast into the sauce. Season with salt and pepper, then let the sauce simmer on low heat for 5 to 10 minutes until it thickens nicely.
Drain the pasta thoroughly and transfer it into the skillet. Toss everything together with the baby arugula until the arugula wilts and is well mixed with the sauce.
Sprinkle the chopped flat-leaf parsley on top and add vegan parmesan if you like before serving.