Spread the cream cheese over both halves of the toasted bagels. Add the salmon to the bottom halves, then top with the avocado. Squeeze over a little lemon juice and season well.
Heat the oil in a non-stick frying pan. When hot, crack in the eggs, season and cook for 2-3 mins until the white is set and starting to crisp up around the edges. Sit the eggs on top of each bagel base and sprinkle cayenne on each yolk. Top with the other half of the bagel and serve with lemon wedges on the side, for squeezing over.