Line a 15x10x1-inch baking pan with paper towels, set aside. Trim stems and remove any wilted outer leaves from Brussels sprouts. Wash and halve. Bring a large pot of lightly salted water to boiling. Add sprouts. Cook, uncovered, 2 minutes; drain. Immediately plunge Brussels sprouts into a large bowl of ice water. Let sit for 3 minutes or until cool. Drain well. Transfer to prepared baking pan; pat dry.
Meanwhile, in a 12-inch skillet, melt the butter over medium heat. Cook, stirring often, until the butter begins to brown and smells fragrant and nutty, about 5 to 10 minutes (reduce heat to medium-low, if necessary, to prevent burning). Add the Brussels sprouts and salt. Cook, turning occasionally, for 5 minutes. Add apples and thyme; cook 7 minutes more or until Brussels sprouts are browned and apple is slightly tender, stirring occasionally. Transfer to a serving bowl. Sprinkle with toasted walnuts and crushed red pepper, if desired.