Preheat oven to 400 degrees F.
Toss vegetables in a bowl with 3 tablespoons of the olive oil. Spread out in an even layer on a baking sheet and sprinkle with coarse salt and freshly ground pepper. Roast, turning once or twice, until tender and browned (some sprouts will be more browned than others), about 25-30 minutes. Remove from the oven and set aside.
Heat a cast-iron or other skillet over high heat. When the pan is hot, add remaining tablespoon of olive oil and the butter. When the butter has melted, reduce heat to medium and add the shallots. Cook, stirring occasionally, until soft and fragrant, 2-3 minutes. Add the wine and cook, still over medium heat, until the liquid reduces by half, about 1 minute.
Turn heat down to low, add the cream, and stir it around. Add the vegetables to the skillet, and cook, stirring occasionally, until they are warmed through and coated with the sauce, 2-3 minutes.
Serve warm, seasoned to taste with Aleppo pepper, cayenne pepper, or crushed red pepper, and more coarse sea salt.