Preheat the oven to 450 degrees F.
Toss the mushrooms with 2 tablespoons olive oil, 1 tablespoon vinegar, the sea salt and pepper. Spread them out in a single layer on a baking sheet and bake until brown, crisp and completely tender, about 10 minutes.
Cook the linguine in salted boiling water until al dente. Drain.
Meanwhile, heat the remaining 4 tablespoons olive oil in a nonstick wok over medium-high heat. Fry the Kashmiri chili powder, Szechuan peppercorns, garlic and fresh chile
until fragrant. Throw in the sugar snap peas, tamari, raw sugar, white parts of the onions, the tomatoes and the remaining 1 tablespoon vinegar. Saute vigorously until the tomatoes are saucy, 8 to 10 minutes. Throw in the shrimp and cook until pink and beginning to curl. Turn the heat down to medium, add the linguine and toss until the pasta has absorbed the sauce, 1 to 2 minutes.
Make a nest of linguine on each plate, leaving a hole in the middle. Place the mushrooms in the center, top with the shrimp and sprinkle with the green parts of the onions and the sesame seeds.