Preheat oven to 400°F. Line 2 large baking sheets with parchment. In a saucepan, combine milk, butter, salt, pepper, onion powder and thyme and bring to a boil. Remove from heat, add flour and stir vigorously with a wooden spoon until combined. Return to heat and cook, stirring vigorously, until a dough forms and pulls away from side of pan
Remove pan from heat and let cool for 5 minutes. Add 4 eggs, 1 at a time, beating well after each addition. Dough will come apart with each egg and then come back together as you stir; add next egg after dough comes back together. You should end up with a sticky dough. Beat in cheese.
Drop dough by teaspoonfuls onto baking sheets. Beat remaining egg with 1 Tbsp. water and brush mixture on dough to glaze. Bake for 10 minutes, then lower temperature to 350°F and bake 20 to 25 minutes longer, until golden brown. Serve hot or at room temperature.