Roasted Brussels Sprouts with Shallots and Wild Mushrooms

For those who don't like brussels sprouts, this preparation may convert you to "the other side". I think one of the tricks is to use previously frozen brussels sprouts. I feel like it cuts the bitter taste to them and tones down the cabbage-like flavor.
For brussels sprouts

• 3 lb Brussels sprouts (preferably frozen), halved lengthwise (if using frozen, gently thaw them first)
  
• 1/4 cup olive oil
• 1/2 tablespoon minced garlic
• 1 teaspoon salt

For shallots

• 2 Tablespoons olive oil
  
• 1/2 lb large shallots (about 6), cut crosswise into 1/8-inch-thick slices and separated into rings (2 1/2 cups)

For mushrooms

• 3/4 stick (6 tablespoons) unsalted butter
• 1 1/4 lb mixed fresh wild mushrooms such as chanterelle and oyster, trimmed, quartered if large
• 1/4 cup dry white wine
• 1 tablespoon chopped fresh thyme
• 1/2 teaspoon salt
• 1/4 teaspoon black pepper
• 1/2 cup water

Preparation

Roast brussels sprouts:
Put oven rack in upper third of oven and preheat oven to 450°F.

Toss Brussels sprouts with oil, garlic, salt, and pepper, then spread out in 1 layer in 2 large shallow baking pans (17 by 12 inches). Roast, stirring occasionally and switching position of pans halfway through roasting, until tender and browned, 25 to 35 minutes.

Carmelize shallots while brussels sprouts roast:
Heat oil in a 10-inch heavy skillet over moderate heat. Cook shallots until golden brown, about 10 minutes.

Sauté mushrooms and assemble dish:
Heat 5 tablespoons butter in skillet over moderately high heat until foam subsides, then sauté mushrooms, stirring occasionally, until golden brown and tender, about 7 minutes.

Add wine, thyme, salt, and pepper and boil, uncovered, stirring occasionally, until liquid is reduced to a glaze, about 2 minutes. Add water (1/2 cup) and remaining tablespoon butter and simmer, swirling skillet, until butter is melted. Transfer to a serving dish and stir in Brussels sprouts. Sprinkle with some of shallots and serve with remaining shallots on the side.