For the crepes: Combine the milk, flour, sugar, salt, eggs and 2 tablespoons of the butter in a blender and blend until smooth, about 20 seconds. Let the batter rest at room temperature for at least 15 minutes before using or transfer to a container with a lid and let rest in the refrigerator for up to 1 day.
For the mustard sauce: Whisk together the creme fraiche, Dijon, whole-grain mustard and some salt and pepper in a bowl. Set aside.
Mix the parsley, chives and dill into the crepe batter. Heat a 10-inch nonstick skillet over medium heat. Lightly brush with some of the remaining melted butter. Add 3 to 4 tablespoons of batter and swirl the skillet so the batter completely covers the bottom. Cook until the underside of the crepe is golden brown, 2 to 3 minutes. Loosen the edge of the crepe with a rubber spatula, then with your fingertips, quickly flip. Cook 1 minute more. Slide the crepe out of the skillet and repeat with the remaining batter, coating the skillet with butter as needed. Stack the finished crepes directly on top of each other.
For the ham and cheesy egg filling: Put the crepes on a plate. Smear each one with a little mustard sauce (leaving some for topping each crepe too), scatter some cheese on top and then put 2 pieces of ham over the cheese.
Whisk the eggs in a bowl with some pepper. Melt the butter in a medium nonstick skillet over medium heat. Add the eggs and cook, stirring, until soft curds form, 2 to 3 minutes. Just before they set, stir in some salt.
Spoon some scrambled eggs over each crepe, leaving a 2-inch border at the top and bottom, then smear on a bit more sauce and scatter on some parsley leaves. Fold the crepes over the eggs so the edges meet in the center and serve immediately.
If you prefer frying the eggs, melt the butter in a nonstick skillet over medium-high heat until the foam subsides, then slip in the eggs, cover and cook until the whites are set and the yolks are still runny, about 3 minutes. Smear the crepes with some of the mustard sauce, scatter the cheese on top and then top with ham. Fold each crepe in half and top with a fried egg, some salt, pepper, sauce and chopped chives.