Heat olive oil in a Dutch oven over medium heat.
Add mushrooms and cook for 5-8 minutes or until they are softened.
Reduce heat to medium-low and add shallots, thyme, and pinch of salt and pepper.
Stir occasionally and cook for 2-3 minutes until shallots are translucent.
Add vegetable broth and simmer for 5-7 minutes.
Meanwhile, bring a pot of salted water to a boil and cook capellini for 2-3 minutes max. Reserve 3/4 cup pasta water.
Using tongs, transfer capellini to the Dutch oven with mushrooms and add 3/4 cup pasta water.
Increase heat to medium and cook for another 2 minutes or until liquid thickens a bit.
Add heavy cream and cheese and stir for another minute until pasta is coated.
Remove from heat and stir in butter.
Optional: Serve with fresh thyme and more parmigiano reggiano on top and season with black pepper.