• Put on a pot of salted water to boil. 

Then prepare the pesto:

• Place garlic and basil in food processor and pulse a few times to get it chopped up. Add the remaining ingredients and blend until relatively smooth, scraping down the sides with a spatula to make sure you get everything. Add a little more vegetable broth if it seems too stiff. Set aside until ready to use.
• Preheat a large pan over medium heat. At this point your pasta water should be ready, so add the linguine.
• Saute onion in oil for about 5 minutes. Use a little cooking spray as needed, or a splash of water if you prefer. Mix in mushrooms, garlic, thyme and salt. Cover pot and cook 5 more minutes, stirring occasionally.
• The pasta should be ready now, so drain it.
• When the mushrooms have cooked down, add pasta to the pan, along with the pesto. Use a pasta spoon to stir and coat the linguine. Get everything good and mixed and the pesto heated through, about 3 minutes. The pesto should be relatively thick, but if it’s too thick (not spreading out and coating the pasta) add a few tablespoons of water. Taste for salt.
• Serve immediately, garnished with a little fresh chopped basil.