Divide goat cheese into 4 or 8 equal portions and shape into 1/2-inch-thick rounds. Place goat cheese rounds in a shallow glass dish; drizzle with 1/4 cup olive oil, and turn to coat completely. Top with thyme sprigs. Cover and refrigerate for 8 hours or overnight.

Preheat oven to 400°F. Stir together breadcrumbs and dried thyme in a small bowl. Remove cheese rounds from oil, and coat thoroughly with breadcrumb mixture. Transfer to a lightly greased baking sheet. Bake in preheated oven until golden brown and bubbly, 10 to 12 minutes.

Meanwhile, place vinegar in a small bowl and season with salt and pepper; whisk in remaining 1/2 cup oil.

Toss lettuce leaves with vinaigrette to lightly coat. Mound dressed lettuce on each of 4 plates. Top each with warm goat cheese rounds. Serve immediately with croutons.