Warm the croissants in a 325°F oven for 4 minutes, then split them.
Cook the bacon until crisp (or warm the ham). Mix the mayo and Dijon.
Beat the eggs with the crème fraîche and a pinch of salt. Melt the butter over low heat and stir the eggs slowly until soft curds form, 3 minutes. Fold in the Gruyère off the heat.
Spread the Dijon aioli inside each croissant, fill with eggs and bacon, and finish with chives and pepper.
Tips
Low heat keeps the eggs custardy so they don't squeeze out.
Avocado and chipotle cream cheese turn it into the Cali Club.