Fill a medium saucepan halfway with water. Bring to a rolling boil and gently add the whole eggs. Boil for 9 minutes then immediately transfer to a bowl of icy water to stop the cooking. Let the eggs cool completely, then peel and set aside.
Place a large piece of parchment on your work surface. Arrange 8 bacon slices horizontally on the parchment. The edges of the slices should touch but not overlap. Working with the remaining 7 slices and stretching each slightly to make it the length of the 8 slices, weave the bacon in an over-under pattern to create a woven lattice design.
Turn the parchment paper so that one of the short sides is in front of you. Using your hands, spread and press half the sausage in an even layer over the bacon. Next, lay 4 slices of ham on top of the sausage, overlapping the pieces slightly and leaving a 1-inch border around the edge between the sausage and ham. Cover the ham with the American cheese slices in a single layer, overlapping the cheese slightly if needed. Cover the cheese with another layer of ham.
Arrange the remaining sausage lengthwise in the center of the ham. Press it into a 5-by-9-inch rectangle positioned crosswise across the center of the ham (the longer side of the sausage rectangle should be in front of you). Put the eggs in a line down the center of the sausage rectangle, so that the tips are touching. Fold the sausage rectangle up and over the top of the eggs so they are encased. Using the parchment under the bacon as a guide, wrap the layered meat around the egg-filled sausage to form a roll; arrange with the seam on the bottom and shape the roll to be as round of a cylinder as possible. Wrap the parchment paper tightly around the rolled meat, transfer to a baking sheet and wrap in plastic wrap. Chill for at least 1 hour and up to overnight.
Prepare a grill for medium indirect heat: For a gas grill (with 3 or more burners), turn all the burners to medium-high heat; after about 15 minutes turn off one of the middle burners and turn the remaining burners down to medium. For a charcoal grill, bank one chimney starter-full of lit and ashed-over charcoal briquettes to one side of the grill. Set up a drip pan on the other side to avoid flare-ups. (Be sure to consult the grill manufacturer's guide for best results).
Place the meat roll seam-side down over the indirect heat side of the grill. Cover and cook until the bacon is browned, about 20 minutes. Turn the roll and cook seam-side up until golden all over and cooked through, about 20 minutes more. Transfer the roll to the direct heat side of the grill and cook, turning the roll once, so the bacon crisps, 1 to 2 minutes per side. Transfer the roll to a cutting board and let rest for 5 to 7 minutes. Cut into thick slices and serve sandwiched in the cinnamon rolls.
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