In a small bowl mix together vinegar and the Dijon mustard. Add the oil in a slow, steady stream, mixing constantly as you pour. Season with salt and pepper. Place the greens in a large bowl.
Arrange the sliced bread on a baking sheet and top the slices with goat cheese. Place under a hot broiler. Toast until the cheese has started to melt and the bread turns brown.
Drizzle the greens with vinaigrette and toss to combine.
Divide the greens onto four serving plates and place three pieces of the toasted cheese bread onto each plate.
Serve immediately while the cheese is still good and hot.