Grease a small square container with butter or cooking spray. Add the almond and coconut flours, baking powder, and salt, and stir with a fork. Add the egg and whipping cream and whisk well, until there are no more lumps. Tap the container on the counter to get rid of bubbles, and microwave for 90 seconds to 2 minutes, until it's cooked through. Slice down the center to create two thinner slices of bread.
Put two slices of ham and two slices of turkey on the bottom slice of bread, add the cheese, then top with the other slice of bread.
Melt the butter in a non-stick skillet over medium-low heat. In a container larger than the sandwich, whisk together the remaining egg, cream, cinnamon, salt, and sweetener if you'd like it. Dip the sandwich in the batter, turning multiple times to soak in as much of it as possible. Fry the sandwich in the butter, about 3 minutes per side, until golden brown. If needed, put a lid on the pan for the last minute or so to ensure the cheese melts.
Cut on the diagonal and serve with your low-carb jelly or syrup of choice on the side for dipping.
Macros per serving, not counting dipping sauces: 601 calories, 32 grams protein, 50 grams fat.