In a large skillet over medium heat, add the vegetable oil and diced onion. Let the onion cook until soft.
Add the garlic and sliced mushrooms and stir to combine. Let the mixture cook for 1-2 minutes.
Add the chicken broth, wine, milk and black pepper. Stir to combine, cover, and bring the mixture to a boil.
Break the linguine in half (so they fit better in the pan), stir into the skillet, and cover with a lid. Keeping the skillet covered, cook the noodles until they are soft, stirring every couple minutes so the noodles do not stick together. This will take about 15 minutes (majority of the moisture will have been soaked up by the noodles). If the mixture is out of liquid before the time is up, add a couple more tablespoons of broth.
Remove the lid and stir in the spinach. Let cook for 2 minutes to soften the spinach. Stir in the grated Parmesan and serve warm.
Serve with additional Parmesan, if desired.
Notes
*The wine can be replaced with an additional 1/4 c chicken broth