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.
½teaspoon vegetable oil
1tablespoon unsalted butter
1teaspoon minced fresh rosemary
¼teaspoon table salt
¼cup red wine
1tablespoon cider vinegar
½cup chicken broth
1. Cook mushrooms and water in 12-inch nonstick skillet 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. Season with salt and pepper to taste, and serve.