Cut bread into ¾"/2cm slices (or buy texas toast style pre-sliced) and preheat oven to 375F/190C.
Preheat large saute pan over medium heat.
Heat another nonstick pan over med-low. Add 3-4Tbsp butter to melt. Brush melted butter to coat both sides of bread slices then transfer bread into preheated large saute pan to toast for 1min - press down with a spatula for max contact and browning.
Flip bread to second side and add 2 slices of ham on each piece of toast, top the ham with a piece of gruyere on each piece of toast.
While second sides of bread toast, add egg into the nonstick that you melted butter in (over med heat) and season with pinch of salt. Cook for 20-30sec then load nonstick egg pan and the saute pan with toast into preheated 375F/190C oven for about 1 min.
Egg is done when white is set and yolk is still gooey. Toast is finished when cheese is fully melted. Combine melty sides of toast (cheese in the middle).
To finish, top with warm mornay sauce, the cooked egg, and garnish with minced chives and black pepper.