In a food processor or blender, combine sun dried tomatoes (and its oil marinade), olive oil, garlic, basil, walnuts, cheese, and all the seasonings. Pulse until it creates a paste-like consistency to create the pesto. Pesto will look slightly gritty from the walnuts and tomatoes.
Boil pasta in salted water (at least 1 tablespoon of salt) and cook according to package instructions or until al dente (slightly undercooked). Turn off heat and do not drain pasta or the water out. Strain out pasta directly from the liquids and transfer to a large mixing bowl or a medium-sized pot (set on low heat on stovetop if you wish to serve warm - see notes). Stir in the pesto paste and fold in with the pasta until well combined.
Scoop out about ½ cup (118ml or more) of pasta water and stir with the final dish.
Garnish with fresh basil, lemon zest, pepper flakes, and vegan shredded cheese.