Preheat oven to 375 degrees F (190 degrees C). Lightly grease a baking sheet.
Unroll each tube of crescent dough, but do not separate rectangles. Place side-by-side on prepared baking sheet with long sides touching; press and seal seams and perforations. Arrange ham lengthwise down center third of rectangle.
Beat cream cheese and milk in a bowl. Separate one egg, placing egg white aside. Stir egg yolk, remaining eggs, salt, and pepper into cream cheese mixture; fold in red pepper and onion.
Melt butter in a large skillet over medium heat; pour egg mixture into skillet and cook until just set, about 5 minutes. Remove from heat and spoon eggs over ham; sprinkle with Cheddar cheese.
Cut 1-inch-wide strips towards the center to within 1/2-inch of filling on each long side of dough. Starting at one end, fold alternating strips at an angle across filling; pinch ends to seal and tuck under. Beat reserved egg white and brush over dough.
Bake in preheated oven until golden, 25 to 28 minutes.