Boil a salted pot of water and cook the pasta al dente according to package directions.
Add the oil and 1 tablespoon of the butter to a skillet over medium-high heat. Once the pan is hot, add the onions and mushrooms. Sauté, stirring occasionally, until the water has been released from the mushrooms & cooked off and everything gets a good sear and is browned/caramelized (this gives a ton of flavor). It’ll take 8-10 minutes or possibly a bit longer.
Stir in the rest of the butter, plus the garlic and Dijon mustard. Cook for about a minute.
Add in the broth and lemon juice + zest, and let it bubble for about a minute or so.
Take the pan off the heat and stir in the parmesan cheese and parsley. Add a splash of the hot pasta water prior to draining the pasta (a couple tablespoons) and then toss the pasta with the sauce. Season with salt & pepper as needed and serve immediately.