Bring a large pot of heavily salted water to a boil and add pasta. Cook for one to two minutes less than the manufacturer's instructions.
While the pasta is cooking, add 2 tablespoons of extra virgin olive oil and the garlic to a large skillet. Turn the heat to medium-low and allow the garlic to slowly toast as the oil warms. Once the garlic is a golden brown colour, remove it from the skillet using a slotted spoon and set aside.
Add a bit more oil to the pan, if needed, and add your sliced mushrooms along with a generous pinch of salt. Cook the mushrooms, stirring and tossing frequently, until they have shrunk down and browned significantly, about 5-7 minutes.
Ladle about 100ml of pasta cooking water into the skillet with the mushrooms and, once pasta is cooked, use tongs to add it to the skillet (do not drain the pasta water). Sprinkle Parmigiano Reggiano cheese over the pasta and toss until the cheese has emulsified with the pasta water and a homogenous sauce forms. Add more pasta water if needed to achieve the right consistency.
Turn off the heat and add reserved toasted garlic and parsley to the pasta. Toss to combine and serve immediately, topping with more Parmigiano if desired.