Whisk together the eggs, milk, cream, orange juice, vanilla, cognac, granulated sugar, cinnamon, nutmeg and a pinch of salt in a bowl.
Place the bread in 2 shallow baking dishes in a single layer.
Pour the egg mixture over the bread; let soak for 10 minutes.
While the bread is soaking, preheat a grill to medium.
Place a flat cast-iron skillet on the grill.
Brush the bananas with the melted butter; cook in the skillet until they are browned on all sides and beginning to release their juices, about 3 minutes. Use a spatula to transfer the bananas to a plate, then wipe the skillet clean with a paper towel. When the bananas are cool enough to handle, cut into 1/2-inch-thick slices.
Remove a piece of bread from the egg mixture, allowing the excess to drip off.
Place on a cutting board, top with four or five banana slices, then cover with another piece of bread.
Brush the skillet on the grill lightly with vegetable oil.
Add the sandwich to the pan; place a grill press or heavy pan over the sandwich to weigh it down. Cook until the bread is nicely toasted and golden, 3 to 4 minutes. Flip, press and cook on the other side until golden. Keep warm; repeat with the remaining bread and bananas, adding more oil as needed.
Transfer the panini to plates and slice in half diagonally; top with confectioners' sugar and plenty of maple syrup.
