Heat a skillet over medium heat.
Remove casings from the chicken sausages and crumble the meat directly into the hot pan.
Cook for 6–7 minutes, breaking up the sausage with a spatula, until browned and cooked through (no pink should remain).
Transfer cooked sausage to a plate and keep warm.
In the same skillet, melt 1 tbsp butter, letting it foam slightly.
Crack in the eggs one at a time. Cook sunny-side-up (whites set, yolks runny) or flip gently for over-easy.
Season lightly with salt and pepper. Remove once cooked to your liking.
While eggs cook, split the bagels and toast them until golden and slightly crisp, either in a toaster or on a skillet.
On each bottom half of a toasted bagel, spoon a generous layer of cooked chicken sausage.
Lay a slice of cheddar cheese on top of the hot sausage so it starts to melt.
Place the fried egg on top of the cheese.
Cap with the top half of the bagel.
Serve sandwiches hot, with deli mustard or hot sauce on the side for extra kick.
Pair with a hot coffee or a cold orange juice for the full New York deli breakfast experience.