While endive is braising, melt butter in a saucepan over medium heat. Add flour and cook, whisking, until a smooth, golden-brown paste (roux) forms, about 3 to 5 minutes. Reduce heat to low, whisk in milk in a slow stream, and cook, stirring, 5 minutes more. Add mustard and continue whisking. Add cheese and continue whisking until completely melted into sauce, about 2 to 3 minutes. Stir in salt, nutmeg, and cayenne. Cook another 3 to 5 minutes, whisking occasionally, until mixture has thickened. Set aside.