Place the eggs into a saucepan in a single layer and fill with water to cover the eggs by 1 inch. Cover the saucepan and bring the water to a boil over high heat. Once the water is boiling, remove from the heat, cover, and let the eggs stand in the hot water for 15 minutes. Pour out the hot water, then cool the eggs under cold running water in the sink. Peel once cold, and cut into 1/4-inch thick slices.
Preheat an oven to 350 degrees F (175 degrees C).
Melt 1 tablespoon of butter in a skillet over medium heat. Cook and stir the onion in the butter until the onion has softened and turned translucent, about 5 minutes. Spread the onion evenly into a 9x13-inch baking dish. Arrange sliced eggs over top, and sprinkle with the Swiss cheese. Whisk the condensed soup and milk together in a bowl until smooth. Season with mustard, seasoned salt, dill, and black pepper. Pour the mixture over the eggs. Butter the rye bread with 2 tablespoons of softened butter, and cut each slice into quarters. Place on top of the casserole, butter-side-up, overlapping if necessary.
Bake in the preheated oven until the bread is beginning to brown and the casserole is hot, 30 to 35 minutes.