Bring a large pot of salted water to a boil. Add the dry pasta and cook until al dente, following the package directions. Reserve a couple tablespoons of the pasta water before draining the pasta, then set pasta aside.
Heat the olive oil and 1 tablespoon of butter in a skillet over medium-high heat. Once hot, add the finely chopped onion and sliced cremini mushrooms. Sauté, stirring occasionally, until the mushrooms release their moisture, the liquid cooks off, and everything is browned and caramelized, about 8–10 minutes or slightly longer.
Lower the heat to medium. Add the remaining 2 tablespoons of butter, minced garlic, and Dijon mustard to the skillet. Cook, stirring, for about a minute until fragrant. I really like how Dijon gives the sauce a subtle depth—don’t skip it if you enjoy a gentle tang.
Pour in the chicken broth (or vegetable broth or white wine), then add the lemon juice and lemon zest. Let the mixture bubble for about a minute to slightly reduce and meld the flavors.
Take the skillet off the heat. Stir in the freshly grated Parmesan cheese and chopped parsley. Add a couple tablespoons of the reserved hot pasta water to help the sauce coat the pasta. Add the drained pasta and toss everything together until well combined. Season to taste with salt and black pepper, then serve immediately.