Brussels Sprouts with Shallots and Wild Mushrooms

INGREDIENTS

• 1 tablespoon chopped fresh thyme
• 1/2 teaspoon salt
• 3/4 stick (6 tablespoons) unsalted butter
• 1 cup vegetable oil
• 3 lb Brussels sprouts, trimmed and halved lengthwise
• 1/4 cup dry white wine
• 1/2 lb large shallots (about 6), cut crosswise into 1/8-inch-thick slices and separated into rings (2 1/2 cups)
• 1/4 teaspoon black pepper
• 1 teaspoon salt
• 1 1/4 lb mixed fresh wild mushrooms such as chanterelle and oyster, trimmed, quartered if large
• 1/2 tablespoon minced garlic
• 1/4 cup olive oil
• 1/2 cup water