Special equipment: a clean kitchen towel or a piece of cheesecloth
For the cinnamon rolls: Preheat the oven to 350 degrees F. and put a rack in the center. Spray a baking sheet with cooking spray and place the cinnamon rolls on the baking sheet, leaving at least 2 inches of space around each. Bake the rolls until golden brown and cooked through, 15 to 20 minutes. Cool slightly on the baking sheet.
Meanwhile, put the bacon in a medium skillet over medium heat and cook, flipping occasionally, until most of the fat has rendered and the bacon is crispy, 15 to 20 minutes. Transfer the bacon to a plate, cool completely, and then chop or crumble it into fine pieces.
Once the cinnamon rolls have cooled slightly, use a serrated knife to split each one in half to resemble a hamburger bun. Whisk together the egg whites and buttermilk in a small baking dish or mixing bowl. Spray a large cast-iron skillet or griddle set between medium and medium-high heat with cooking spray. In batches, lightly dip the cut side of each cinnamon roll in the egg mixture and cook, cut-side down, until the egg is just set and light golden brown, 2 to 3 minutes. Remove to a baking sheet cooked-side up.
For the turkey patties: Put the turkey, apple, onion powder, red pepper flakes, fennel seeds, sage and 1 tablespoon salt in a mixing bowl. Mix with your hands until just combined. Divide the mixture into sixteen 2-ounce portions and use your hands to shape each portion into a large meatball. Put the meatballs on a baking sheet.
Spray a large cast-iron skillet or griddle over medium-high heat with cooking spray. In batches, add the meatballs and use a large metal spatula to flatten them into thin patties. Cook until the first side is lightly browned, about 2 minutes, then flip and cook on the other side until lightly browned and just cooked through, 1 to 2 additional minutes. Remove the patties to a large plate or baking sheet.
For the hash browns: Put the grated potatoes and parsnips on a clean kitchen towel or piece of cheesecloth, roll it up and wring out as much liquid from the vegetables as possible. This is very important because you want them to be as dry as possible.
Shake the vegetables into a mixing bowl, add 1 teaspoon salt and 1/4 teaspoon pepper, and mix until well combined. Divide the mixture into sixteen 2 1/2-ounce portions and put on a baking sheet.
Heat 1 tablespoon of olive oil in a large cast-iron skillet or griddle over medium heat. In batches of 4, cook the hash browns on one side, undisturbed, until golden brown and crispy on the bottom, about 4 minutes. Flip the hash browns over and cook until golden brown and crispy on the other side, about 4 additional minutes. Remove the cooked hash browns to a large plate or baking dish, making sure not to stack them, which would make them soggy. Cook the remaining hash browns, adding 1 additional tablespoon of olive oil before cooking each batch.
For the burger assembly: If necessary, warm the cinnamon roll glaze so it is loose enough to drizzle. Layer on the bottom half of a warm cinnamon roll, cut-side up: 1 piece of green leaf lettuce, 1 turkey patty, 1 hash brown, another turkey patty, 1 tablespoon cream cheese, another hash brown and 1 slice of tomato. Top with the other half of the cinnamon roll, cut-side down. Drizzle the top with 1 1/2 teaspoons of glaze and sprinkle with 1/8 of the bacon pieces. Repeat this process to make 7 additional burgers. Serve immediately.