Preheat oven to 350°. Toast hazelnuts on a rimmed baking sheet, tossing once, until golden brown, 8–10 minutes. Let cool, then coarsely chop.
Place cherry tomatoes in a large bowl; season with salt.
Cook spaghetti in a large pot of boiling salted water, stirring occasionally, until al dente. Drain pasta, reserving ¼ cup pasta cooking liquid.
Meanwhile, purée beefsteak tomato, garlic, red pepper flakes, ½ cup basil, 3 Tbsp. chopped hazelnuts, and 1 tsp. salt in a food processor until smooth; add to bowl with salted cherry tomatoes.
Add zucchini, spaghetti, pasta cooking liquid, ¼ cup oil, and remaining ½ cup basil leaves and toss to combine; season with salt and pepper.
Divide pasta among bowls, drizzle with more oil, and top with vegan parm and remaining hazelnuts.