Step 1Place chives, thyme and cheese in processor bowl. Process until cheese is coarsely chopped; set aside on foil. Do not wash bowl.
Step 2Bring water, 1/3 cup milk, butter, salt, nutmeg and pepper to boil in small saucepan over medium heat. Remove pan from heat. Use wooden spoon to vigorously stir in flour until mixture is well combined and leaves side of pan, about 1 minute. Return to heat and cook, stirring often, 2 minutes.
Step 3Transfer dough to processor bowl. Turn on processor and add 4 eggs through feed tube, stopping once to scrape down sides, until mixture is thick and smooth, about 20 seconds. Add remaining milk; process 5 seconds. Add reserved cheese mixture; process 5 seconds more.
Step 4Grease 2 baking sheets and sprinkle lightly with water (steam will release puffs from pan after they are baked). Put dough into pastry bag fitted with 3/4-inch-wide tube; pipe into 1 1/4-inch rounds on pans with 1-inch spacing. Alternately, use tablespoon to place rounds onto pan, pushing dough off with your finger. Use your finger to dab egg wash onto puffs, smoothing any rough edges.
Step 5Bake at 400 degrees until golden brown, about 15 to 20 minutes. Use spatula to transfer to wire racks to rest 10 minutes. Serve warm. (Can be baked several hours ahead and kept at room temperature; reheat in 300-degree oven 8 minutes and serve warm. Or, arrange puffs in single layer on baking sheets and freeze. Frozen puffs can then be packed in airtight bags and frozen up to 1 month. Reheat unthawed puffs, uncovered, in single layer on baking sheet in 300-degree oven 10 to 12 minutes. Serve warm.)