Position a rack in the center of the oven and heat the oven to 450°F.
Put the Brussels sprouts on a rimmed baking sheet, and drizzle with 3 Tbs. of the olive oil; toss to coat. Spread the Brussels sprouts in an even layer and season generously with salt. Roast until tender and browned, about 25 minutes. Remove from the oven and set aside.
Heat a 12-inch skillet over high heat. When the pan is hot, add 1 Tbs. of the olive oil and 2 Tbs. of the butter. When the butter has melted, add the mushrooms in an even layer, and cook, stirring occasionally, until the mushrooms are golden-brown and tender and the mushroom liquid (if any) has evaporated, 5 to 8 minutes. Season to taste with salt and transfer to a plate.
Set the skillet over medium-high heat and add the remaining 1 Tbs. olive oil and 1 Tbs. butter. When the butter has melted, add the shallot, season with a pinch of salt, and cook, stirring occasionally, until tender and golden, 3 to 4 minutes. Add the wine and cook until reduced by half, about 1 minute. Return the mushrooms to the pan and add the Brussels sprouts and cream. Stir in a few grinds of pepper and continue to cook, stirring occasionally, until the cream thickens and coats the vegetables nicely, 3 to 4 minutes. Season to taste with salt and pepper. Serve immediately.
Make Ahead Tips: The brussels sprouts can be roasted and the mushroom seared up to 8 hours ahead. Make the sauce and finish the dish just before serving.