Start by putting the oven rack into the center of the oven and preheat to 450°F.
Prepping and Roasting the Brussels Sprouts
While the oven is preheating, place the Brussels sprouts in a large bowl and top with 3 tablespoons of olive oil and 2 tablespoons of the butter. The original recipe has you do this on a rimmed baking sheet, but I find it easier and more efficient to work in a bowl. Yes, one more thing to clean but I think you get better coverage.
Spread the Brussels sprouts onto a rimmed baking sheet, season with salt and roast in the oven for about 25 minutes or until the Brussels sprouts are nicely brown and fork tender. Remove from the oven and start preparing the mushrooms.
Sautéing the Mushrooms
Heat a large fry pan (skillet, sauté pan) over high heat until sufficiently hot.
Add 1 tablespoon of olive oil, 2 tablespoons of butter and then the mushrooms in a single layer. Cook until the mushrooms are golden-brown and all the liquids from the mushrooms has evaporated. This takes about 8 minutes.
Season with salt to taste, transfer to a plate and reserve.
Finish the Dish
Reheat the large fry pan over medium high heat and add the remaining 1 tablespoon of olive oil and 1 tablespoon of butter.
Add the shallot, a pinch of salt and cook for about 3 to 4 minutes until the shallot is tender.
Add the white wine and continue cooking until the wine is reduced by half.
Add the mushrooms back to the pan along with the Brussels sprouts and heavy cream. Give everything a stir, taste and adjust seasoning with salt and pepper.
Let this cook for another 4 minutes or until the cream thickens to your desired consistency.
Again taste and adjust seasoning with salt and pepper if needed.
Serve right away.
If you're asking yourself how did my wife roast the Brussels sprouts on the center rack next to a big turkey, she didn't. She roasted the Brussels sprouts first and got them ready for the second phase of cooking - sautéing.