Preheat oven to 350 degrees. Spread walnut halves on a rimmed baking sheet. Toast until fragrant, about 10 minutes, stirring at 5 minutes.
Melt 4 tablespoons vegan butter in a small skillet. Add the bread crumbs, cook until lightly toasted, 3 to 4 minutes. Remove from the heat and set aside.
Meanwhile, cook linguine in a pot of boiling salted water until al dente, according to package instructions. Drain; return to pot. While still very hot, stir in chopped spinach to wilt slightly.
Process half of walnuts, soy milk, nutritional yeast, lemon juice, garlic and melted butter in a blender until smooth. Taste and seasoning with salt and pepper. Toss with pasta, remaining walnuts, red pepper flakes, and parsley.