Bring a large pot of salted water to a boil. Add the pasta and cook to al dente, according to the package directions. Reserve 1 cup of pasta water if you anticipate leftovers (see note). Drain and set aside.
While the pasta is cooking, heat 1 tablespoon olive oil in a large skillet over medium-high heat, add the mushrooms and sprinkle with a ½ teaspoon of salt. and let them brown, tossing only occasionally, about 3-5 minutes, until the mushrooms have plenty of color and the skillet is dry.
Lower the heat to medium and add two tablespoons of water to the pan, along with the asparagus and another ½ teaspoon of salt. Cook, stirring frequently, until the asparagus is bright green and crisp-tender, about 5 minutes longer. Remove the vegetables from the pan and set aside.
Reduce the heat to medium-low and return the pan to the burner. Add another tablespoon of olive oil. Add garlic and saute about 1 minute, until fragrant. Add the light cream and bring it to a gentle simmer. Simmer for 3-4 minutes until slightly thickened.
Turn the heat down to low and sprinkle in the Parmesan cheese, stirring until smooth. Stir in the thyme, oregano, red chili flakes, lemon juice and zest. Taste and season with more salt and pepper to taste, if needed.
Add drained pasta and vegetables back to the pan and stir to combine. Garnish with more Parmesan, red chili flakes, and fresh basil if desired, and serve.