Preheat oven to 425°. In a 12-in. cast-iron or other ovenproof skillet, melt butter over medium-high heat. Add shallot; cook and stir until tender, 1-2 minutes., In a large bowl, whisk eggs and milk until blended. Whisk in flour, salt and pepper until smooth; stir in thyme. Pour batter into hot pan; sprinkle with Parmesan., Bake until top is puffed and sides are golden brown and crisp, 20-25 minutes. Serve immediately.