With the motor of the food processor running, mince the shallot by dropping it through the feed tube. Add the walnuts, thyme, lemon zest, the salt, paprika, and lemon juice. Pulse until the walnuts are chopped, but not ground, scraping the sides of the work bowl, as needed. With the motor running, pour in the walnut and/or olive oil, all at once. Scrape into a bowl and season with a generous grind of black pepper. Set aside.
Grill the zucchini and cook the pasta:
Preheat the grill. Trim the ends from the zucchini. Slice lengthwise, thinly, about 1/8-inch thick. Toss with olive oil, the salt and plenty of freshly ground pepper.
On a vegetable grilling accessory tray, grill over high heat, turning until lightly charred on the edges and limp tender, 5 to 10 minutes. Transfer to a plate and keep warm.
Cook the pasta in well-salted water, following to package directions. When the pasta is almost done, mix about 3 tablespoons of the pasta water into the walnut pesto.
Drain the pasta and immediately toss with the walnut pesto and grilled zucchini.
Serve hot, with a sprinkle of thyme and basil leaves.
If you wish, serve with grated Parmesan or Romano cheese at the table.