Cook the pasta according to the package instructions until al dente. Reserve about 1/2 cup of pasta cooking water before draining.
In a large dry skillet, on medium heat, toast the walnuts until fragrant. Don't burn or over toast them. (about 3 minutes) Then take them out of the pan and set aside.
Add 1 tablespoon of olive oil to the skillet. Add minced garlic and chopped kale. Sauté for 3-5 minutes until the kale is wilted and tender. Stirring kale several times while cooking.
(optional) If adding tomatoes, add to the kale and garlic pan a minute or two before the kale is done to heat the tomatoes through.
Toss the cooked pasta into the skillet with the kale and garlic. (and tomatoes, if adding). Add toasted walnuts, nutritional yeast, 1 tablespoon extra-virgin olive oil, lemon juice, salt and pepper. Add a bit of the reserved pasta cooking water if needed so that the pasta does not clump and to reach your desired creamy consistency.
Divide the pasta among plates. Garnish with red pepper flakes and vegan Parmesan cheese if desired.
Serve your vegan kale walnut pasta immediately and savor the flavors!