Heat the olive oil and butter in a large skillet or non stick pan overn medium-high heat.
When the oil is shimmering hot and the butter melted, add the mushrooms, salt to taste and fresh black pepper. Toss the mushrooms to coat and then leave them to sear, undisturbed. If necessary, stir occasionally. This should take anywhre between 6 to 8 minutes or until golden brown. If cooking the mushrooms in batches, repeat with the remaining mushrooms.
Meanwhile, bring a large pot of salted water to boil. Cook the pasta according to the package instructions with about a minute or less before al dente. Reserve 1cup of the pasta water just before it's about the reach al dente.
By now, the mushrooms should be cooked and brown. Lower the heat, add the garlic and fresh thyme, toss giving it a minute before adding the balsamic vinegar. As the balsamic cooks in, use a pair of tongs to start transferring the pasta to the mushrooms balsamic. The pasta will come with drippings of the pasta water, that's good, that's what you want, it will emulsify with the fat in the skillet and create a cream so toss it all together.
Keep tossing and adding any of the reserved pasta water if you need it.
Remove from the stove and serve with a drizzle of extra-virgin olive oil, more fresh thyme, ground black pepper, flakey salt and shaved parmesan cheese.