Mix breadcrumbs and thyme on waxed paper. Season goat cheese rounds with salt and pepper. Dip cheese into beaten egg, then into breadcrumbs, coating thoroughly. Place on a rack, cover and refrigerate until ready to use (up to 6 hours).
Whisk vinegar and mustard in small bowl until blended. Gradually whisk in 1/2 cup oil. Season to taste with salt and pepper. Set aside. Heat 3 TBS olive oil in large skillet over medium-low heat. Add walnuts and sauté just until lightly toasted. Remove with slotted spoon and drain on paper towels. Add cheese rounds and cook just until crisp and brown, about 2 minutes per side.
Toss greens with dressing to coat; divide among four plates. Place two cheese rounds on each salad, and garnish with walnuts. 4 servings.