1. Preheat oven to 350 degrees. Line a baking sheet with parchment paper; set aside.

2. Place milk, butter, and 1 teaspoon salt in a large heavy-bottomed saucepan over medium heat. Cook until butter has melted and mixture comes to a boil. Add flour; stir constantly until mixture is smooth and begins to pull away from the sides of the pan, about 3 minutes.

3. Transfer mixture to the bowl of an electric mixer fitted with the paddle attachment. With the mixer on medium speed, add 5 eggs, one at a time, making sure each is fully incorporated before adding the next. Mixture will be thick, smooth, and shiny. Stir in cheese, pepper, and thyme.

4. Using a large spoon, form rounds about 3 inches wide and 1 inch high on prepared baking sheet, spacing each about 2 inches apart. In a small bowl, whisk together remaining egg and pinch of salt. Brush each pastry round with egg mixture and sprinkle with cheese.

5. Transfer baking sheet to oven and bake until puffed, golden brown, and light for their size, 35 to 45 minutes. Remove pastries from oven and poke a small hole in the top of each to allow steam to release. Serve hot, warm, or at room temperature.