Bring a large pot of generously salted water to a rolling boil. Add the spaghetti and cook according to package directions until al dente. Before draining, reserve about 1 cup of the starchy pasta water.

While the pasta cooks, heat the olive oil in a large skillet or Dutch oven over medium-high heat. Add the sliced cremini mushrooms and cook for 5-7 minutes, stirring occasionally, until they are well browned and most of their liquid has evaporated. Do not overcrowd the pan; cook in batches if necessary.

Reduce the heat to medium. Add the minced garlic and red pepper flakes to the skillet with the browned mushrooms. Sauté for another 1-2 minutes until fragrant, being careful not to burn the garlic.

Pour in the vegetable broth (or 1/2 cup of the reserved pasta water) into the skillet. Scrape up any browned bits from the bottom of the pan with a wooden spoon, which will add depth of flavor to the sauce. Bring the mixture to a gentle simmer.

Add the drained spaghetti directly to the skillet with the mushroom and garlic mixture. Toss everything vigorously to combine, ensuring the pasta is thoroughly coated. If the sauce appears too dry, add more reserved pasta water a tablespoon at a time until the desired consistency is reached. Stir in the chopped fresh parsley, the remaining 1/2 tsp salt, and black pepper.

Taste the spaghetti and adjust seasoning as needed. Serve immediately in bowls, garnished with grated Parmesan cheese if desired for an extra savory touch.