Preheat oven to 375 degrees F. Line a baking sheet with foil; set aside.
Working over a medium bowl, press eggs through a cheese shredder or mash with a fork until finely chopped. Add shallot, pickle, parsley, oil, mayonnaise, the 1/2 teaspoon dill, the mustard, celery seeds, and pepper; stir until combined.
Top bagel thin halves or English muffin halves with egg mixture; place on the prepared baking sheet. Sprinkle with cheese. Bake about 5 minutes or until egg mixture is heated through and cheese is melted. If desired, garnish with additional fresh dill. Serve warm.