1. Preheat oven to 425°. Bring first 2 ingredients and 1 cup water to a boil in a large saucepan over high heat. Reduce heat to medium. Add flour all at once, and beat vigorously with a wooden spoon 1 to 2 minutes or until mixture is smooth and pulls away from sides of pan, forming a ball of dough. Remove from heat, and let stand 2 minutes. Stir in eggs, 1 at a time, beating vigorously with wooden spoon after each addition. (Mixture should be smooth and glossy.) Add Cheddar cheese, and stir until well blended.
2. Drop batter by level spoonfuls 1 inch apart onto a parchment paper-lined baking sheet, using a small cookie scoop (about 1 inch). Sprinkle with Parmesean cheese.
3. Bake at 425° for 10 minutes. Reduce oven temperature to 375°, and bake 17 to 20 more minutes or until golden brown.
4. Cut each gougère in half, and fill bottom half with desired amount of Deviled Ham. Top with remaining half.