Preheat the oven to 350°F, line both baking sheets with parchment paper, and grease the parchment paper with butter. For the omelet, whisk together the eggs, shredded cheese, and mayonnaise.
Pour the omelet mixture onto both baking sheets, transfer the baking sheets to the oven, and bake at 350°F for 15–20 minutes. Place 2 clean kitchen towels on your work surface. Once the omelets are done baking, flip the baking sheets over onto the kitchen towels, remove the parchment paper from the top, and let the omelets cool.
For the ground beef filling, stir together the ground beef, diced onion, and spices until combined. Spread an even layer of the ground beef mixture over the surface of the larger omelet, leaving a 4-inch section uncovered. The layer of ground beef should be the same size as the smaller omelet.
Place the smaller omelet on top of the layer of ground beef and place the slices of cheese and baby spinach on top.
Use the kitchen towel to help roll everything up into a snug log.
Transfer the stuffed omelet roll to a baking tray lined with parchment paper, transfer the baking tray to the oven, and bake the omelet roll at 350°F for 25–30 minutes.