Bring a large pot of salted water to a boil. Add spaghetti and cook according to package instructions until al dente. Reserve 1 cup of pasta water, then drain the pasta.

In a skillet over medium heat, add a splash of olive oil. Sauté the garlic for 1 minute until fragrant, then add the mushrooms and asparagus. Cook for about 5-7 minutes until tender.

In a bowl, whisk together the eggs, Parmesan cheese, heavy cream (if using), black pepper, and salt until well combined.

Add the drained pasta to the skillet with the vegetables. Remove from heat and quickly pour the egg mixture over the pasta, tossing to combine. Add reserved pasta water a little at a time until the sauce reaches desired consistency.

Serve immediately, garnished with chopped parsley and additional Parmesan cheese if desired.