Cook the Pasta : Bring a large pot of salted water to a boil. Add the spaghetti and cook according to package instructions until al dente. Reserve ½ cup of pasta water, then drain the pasta and set aside.
Toast the Breadcrumbs : Heat the olive oil in a small skillet over medium heat. Add the breadcrumbs and stir frequently until golden and crisp, about 3-5 minutes. Season with a pinch of salt and black pepper. Remove from heat and set aside.
Brown the Butter : In a large skillet, melt the butter over medium heat. Continue cooking, stirring frequently, until the butter foams and begins to turn golden brown, about 4-5 minutes. Reduce the heat to medium-low, add the minced garlic, and sauté for 1 minute until fragrant.
Cook the Mushrooms : Add the sliced cremini mushrooms and thyme sprigs to the skillet with the browned butter. Cook for 5-7 minutes, stirring occasionally, until the mushrooms are tender and browned. Season with salt and pepper to taste.
Combine Pasta and Sauce : Discard the thyme sprigs and add the cooked pasta to the skillet. Toss to coat the spaghetti in the mushroom and brown butter mixture. Gradually add reserved pasta water, a tablespoon at a time, to loosen the sauce if needed.
Garnish and Serve : Stir in the chopped parsley and adjust seasoning with more salt and pepper if desired. Serve the pasta topped with the toasted breadcrumbs for a delightful crunch.