1. Preheat oven to 425°.
2. 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.
3. Heat remaining 1 tablespoon butter and oil in skillet over medium heat. Sauté 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. Serve remaining sauce on the side.