Place the eggs in a medium saucepan and cover with cold water by at least one inch.
Bring the water to a rolling boil over high heat, then immediately turn off the burner and cover the pan with a lid.
Let the eggs sit in the hot water for 12 minutes to achieve a perfect hard-boiled yolk.
While the eggs cook, prepare an ice bath by filling a bowl with cold water and ice cubes.
Transfer the eggs to the ice bath for 5 minutes to stop the cooking process and make them easier to peel.
Gently crack the eggshells and peel them under cool running water, then slice each egg in half lengthwise.
Remove the stem and seeds from the bell pepper and slice it into thin, uniform strips.
Cut the sharp cheddar cheese into small cubes or thin rectangular slices.
Arrange the egg halves, pepper strips, and cheese on a plate, then season with sea salt, black pepper, and everything bagel seasoning.