Preheat oven to 300 deg. Spread bread crumbs on baking sheet. Bake crumbs for about 10 minutes to dry.
Peel eggs, halve and separate yolks from whites. Melt butter in heavy small skillet over low heat. Add herbs and stir until wilted, about 1 minute. Cool slightly. Mash yolks in small bowl. Stir in herb mixture. Season with salt and generous amount of pepper. Spoon herbed yolk mixture into egg whites.
Combine bread crumbs and Parmesan in shallow bowl. Dip stuffed eggs in flour, then beaten egg; roll in bread crumbs, coating thoroughly. Refrigerate uncovered at least 20 minutes. (Can be prepared 6 hours ahead.)
Heat oil in deep fryer to 360 deg. Fry eggs in batches (do not crowd) until golden brown, turning occasionally, 3 to 4 minutes. Drain on paper towels. Sprinkle with salt and serve.
Combine parsley with sage, rosemary or basil.