2/3cuplow-sodium chicken broth, plus more if needed
3 to 4cupsfresh spinach, roughly chopped (about 3 ounces)
2tablespoonsfresh parsley, chopped
4slicesMuenster or Havarti cheese
Trim any white tendons from the tenderloins and discard.
Combine the flour with 1 teaspoon of salt and a few grinds of black pepper in a zip-top bag. Add the chicken and shake until coated.
Coat the bottom of a large frying pan with vegetable oil and heat on medium-high. Add the chicken in a single layer and cook until barely golden, 1 minute per side. Transfer the chicken to a plate and set aside.
Add the onion to the pan, sauté until soft and translucent, 3 to 4 minutes, then add the garlic.
Continue cooking for another minute, then deglaze the pan with the wine, scraping up any browned bits that may have accumulated on the bottom of the pan.
Reduce the heat to medium, stir in the mushrooms, season with salt and pepper and arrange the chicken tenderloins on top.
Pour the broth over the chicken and as soon as it begins to bubble, scatter the spinach on top and cover the pan.
Continue cooking until the tenderloins are cooked all the way through, 2 to 3 minutes longer. Using a spatula, turn the chicken and incorporate the spinach into the sauce. Taste and adjust the seasoning as needed.
Top with chopped parsley and arrange the cheese slices on top. Cover and cook just long enough to melt the cheese, 1 minute more.