In a small bowl, combine all cream cheese mix ingredients and set aside.
Heat a large grill pan over medium heat. Slice both egg buns in half, and lightly coat all cut-sides with butter. Lay all slices into the grill pan, cut-side down. Grill for 1-2 minutes, until toasted. Remove all buns from grill pan, and set aside.
Spread cream cheese mixture onto the cut-side of both top halves. Place these halves near the untouched bottom halves.
Lay one slice of turkey flat onto the grill pan. Allow to cook for 10-15 seconds, or until steaming and grill lines are apparent. Flip over and repeat on other side. Remove the turkey slice from the grill pan, and immediately place onto one bottom half of an egg bun. Top with shredded cheddar cheese.
Repeat with another turkey slice, and place directly onto the first turkey slice and cheese. Top with a bit more shredded cheddar (if desired), then top with one lettuce leaf. Place top half of egg bun directly onto the lettuce (cream cheese side down to touch the lettuce).
Repeat to make a second sandwich.