Sautéing mushrooms the usual way means piling them in a skillet slicked with a couple of tablespoons of oil and waiting patiently for them to release their moisture, which then must evaporate before the mushrooms can brown. Instead, we accelerate the process by adding a small amount of water to the pan and steaming the mushrooms, which allows them to release their moisture more quickly. The added benefit of steaming them is that the collapsed mushrooms won't absorb much oil; in fact, ½ teaspoon of oil was enough to prevent sticking and encourage browning. And because we used so little fat to sauté the mushrooms, we were able to sauce them with a butter-based reduction without making them overly rich. Adding broth to the sauce and simmering the mixture ensured that the butter emulsified, creating a flavorful glaze that clung well to the mushrooms.
https://www.americastestkitchen.com/recipes/11322-sauteed-mushrooms-with-red-wine-and-rosemary

• 1 lb sliced mushrooms (white, cremini, portobello, shiitake, oyster and maitake)
• 1/4 cup water
• 1/2 tsp oil
• 1 TBSP Butter
• 1 TBSP Minced Shallot
• 1 tsp Rosemary
• 1/8 cup Red Wine
• 1/8 cup Cider Vinegar
• 1/2 cup broth

1. Add mushrooms and water to cold 12-inch nonstick skillet and cook over high heat, stirring occasionally, until skillet is almost dry and mushrooms begin to sizzle, 4 to 8 minutes. Reduce heat to medium-high. Add oil and toss until mushrooms are evenly coated. Continue to cook, stirring occasionally, until mushrooms are well browned, 4 to 8 minutes longer. Reduce heat to medium.
2. Push mushrooms to sides of skillet. Add butter to center. When butter has melted, add shallot, rosemary, salt, and pepper to center and cook, stirring constantly, until aromatic, about 30 seconds. Add wine and vinegar and stir mixture into mushrooms. Cook, stirring occasionally, until liquid has evaporated, 2 to 3 minutes. Add broth and cook, stirring occasionally, until glaze is reduced by half, about 3 minutes.
3. Season with salt and pepper to taste, and serve.

1. Use one variety of mushroom or a combination. Stem and halve portobello mushrooms and cut each half crosswise into ½-inch pieces. Trim white or cremini mushrooms; quarter them if large or medium or halve them if small. Tear trimmed oyster mushrooms into 1- to 1½-inch pieces. Stem shiitake mushrooms; quarter large caps and halve small caps. Cut trimmed maitake (hen-of-the-woods) mushrooms into 1- to 1½-inch pieces. You can substitute vegetable broth for the chicken broth, if desired.