Place cheese in a shallow dish and drizzle with two tablespoons of oil; turn to coat completely. Sprinkle fresh thyme on top. Cover and refrigerate 6 hours or overnight. Preheat oven to 400 degrees and in a small bowl, combine crumbs with dried thyme. Remove the cheese from the oil and coat completely with the crumbs. Transfer to a lightly greased baking sheet. Bake, without turning until golden brown and bubbly, about 10 to 12 minuntes.
Meanwhile, place two tablespoons of the vinegar in a bowl and slowly whisk in the remaining oil. Season with salt and pepper to taste. Add more vinegar, if necessary, to balance the flavors. Toss the lettuce with enough vinegrette to coat lightly and mound the greens on individual plates. Invert a round of warm goat cheese into the center.