Preheat oven to 400 degrees F. Line 2 large baking sheets with parchment paper. Meanwhile, combine butter, salt, milk, pepper, and thyme in a medium saucepan. Bring to a rolling boil. Immediately, remove from heat and add in flour. Stir until contents are mixed thoroughly Return pan to heat, continuing to stir, and cook until dough forms and pulls away from sides. Remove from heat and cool for 5 minutes. Once cool, add in 4 eggs, 1 at a time, mixing well after each addition (result should be a sticky dough). Then, beat in cheese. Spoon tablespoon drops of dough into baking sheets. In a small bowl, beat remaining egg with water. Brush egg wash mixture over the dough balls. Bake dough balls in for 10 minutes in preheated oven. After 10 minutes, reduce the over to 350 degrees F. Continue to bake for another 20-25 minutes until golden brown. Remove from oven and let cool for 5-10 minutes. Serve and enjoy.
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