Mix together the olive oil, garlic, chilli oil and salt in a large bowl. Toss the vegetables (including mushrooms) in the mixture to coat them. Remove the vegetables from the oil and reserve the oil. Grill the vegetables on a medium to high heat for 5 minutes on each side until golden and tender. Return the vegetables to the oil.
Cook the tagliatelle in a pan of boiling salted water for 2 minutes until al dente. Drain the pasta then toss with the vegetables and oil and season.