Bring a large pot of salted water to a boil and drop in your pasta. Cook it just until al dente, following the package timing, since it'll finish cooking a bit more once tossed with the hot sauce. Save about a half cup of the starchy pasta water before you drain it, because that liquid is gold for loosening the sauce later.
While the pasta cooks, melt the butter in your skillet over medium heat and add the diced onion. Let it soften for a couple of minutes before tossing in the sliced mushrooms. Cook everything for about 10 minutes, stirring occasionally, until the mushrooms release their liquid and that liquid cooks back off again.
Once the mushrooms are golden and the pan looks mostly dry, stir in the chopped garlic and thyme. Cook for just a minute, stirring constantly so the garlic doesn't scorch. This is the moment your kitchen starts smelling incredible.
Pour in the white wine and scrape up any browned bits stuck to the bottom of the pan. Let it bubble for about a minute so the alcohol cooks off, leaving behind all that concentrated flavor. If you're skipping wine, broth works fine here too.
Add the broth and heavy cream to the pan, bring it up to a gentle boil, then reduce the heat and let it simmer for 2 to 4 minutes until it thickens slightly. This step sets the stage for the cheese to melt in smoothly instead of clumping.
Remove the pan from the heat and stir in the cubed brie and grated parmesan, along with the miso paste if you're using it. Keep stirring until the cheeses fully melt into a glossy, creamy sauce. Taste it now and adjust the salt and pepper.
Add your drained pasta directly into the skillet and toss everything together, splashing in reserved pasta water a little at a time until the sauce clings to every strand. Serve immediately while it's warm and stretchy.