In a large skillet, heat half the olive oil over medium heat. Add the onion and cook, until they are translucent. Lower the heat to medium low, season with salt and pepper, and continue cooking until caramelized, about 5 minutes. Remove to a small bowl and set aside. Return the pan to the heat, add the remaining olive oil, and turn the heat to high. Add the mushrooms, stirring well to coat with oil. Keep the heat high and sauté the mushrooms, stirring, until they brown lightly, 4 to 5 minutes. Season the mushrooms with sea salt and freshly ground black pepper. Add the garlic, rosemary, thyme, red pepper flakes and tomato paste, stir well to combine. Reduce the heat to medium, add back the onion and stir well to coat. Ladle ¾ cup of the hot mushroom broth into the mushrooms, stirring well and allow to reduce by half. Add the other ¾ cup mushroom broth, stirring gently and let the sauce cook for another 5 minutes.
Meanwhile, bring a large pot of salted water to the boil. Cook the pasta until al dente. Drain pasta and add to the mushroom mixture, tossing gently to coat the pasta with the sauce. Season to taste with salt and black pepper, add the lemon zest and fresh juice, toss well.
Top with vegan cheese if desired and serve immediately.