In a large skillet over medium heat, melt 1 tablespoon of butter. In a wide, shallow bowl, whisk together 1 egg, half and half, salt, cinnamon, and 1 tablespoon of maple syrup. Dip one side of each slice of bread into the French toast egg mixture, being careful to keep the other side of the bread dry. Lay the bread, French toast side down, in the buttered skillet and grill until golden.

While that’s happening, grab another small pan and cook the other egg over easy with a bit of butter so the yolk is still slightly runny. Remove the bread and egg from their pans.

Spread about 1 ½ ounces of softened cream cheese on the “French toasted” sides of your bread slices. Melt the last tablespoon of butter over medium low heat in your skillet. Lay one slice in the skillet so the French toast/cream cheese side is facing up.

Sprinkle ¼ cup cheddar cheese onto the sandwich. Mix the butternut squash puree with a tablespoon of maple syrup and spread half of it on top of the cheese. Then add a sprinkle of thyme, the egg, and the bacon to each sandwich. Follow that with the rest of the butternut squash, more thyme, and another ¼ cup cheddar. Cover with the other slice of bread, so the French toasted cream cheese side is down. Over low heat, grill the sandwiches on each side until golden brown and gooey.