Cut Brussels sprouts in half lengthwise; toss to coat evenly with 2 tablespoons butter, 2 tablespoons olive oil, sea salt, and pepper.
Bake on a 15- x 10- x 1-inch jellyroll pan at 425 for 18 minutes or until Brussels sprouts are tender and outer leaves are golden brown and slightly crispy, stirring halfway through.
Heat remaining 1 tablespoon butter and oil in skillet over medium heat. Saut shallots for 2 minutes or until translucent and cooked through.
Add vinegar; reduce heat to low, and cook 1 minute. Stir in mustard and cream; bring to a low boil.
Let simmer and reduce about 5 minutes or until sauce is thick and creamy. Toss Brussels sprouts with parsley, and drizzle half the warm sauce over the top.