In a small bowl whisk together vinegars, mustard, and sugar. Add oil in a stream, whisking, and whisk vinaigrette until emulsified. Stir in shallot, salt and black pepper.
In a small saucepan melt butter over moderate heat and add walnuts and sugar. Cook walnuts, stirring, until golden, about 2 minutes, and transfer to a bowl.
Cut endives lengthwise into julienne strips. Halve and core apples and cut into julienne strips.
In a large bowl combine endives, apples, walnuts, Stilton, tarragon, and vinaigrette, tossing gently, and season with salt and white pepper.
