Preheat oven to 225°F. Lay 8 slices of bread on a work surface and spread 1 side of each with cream cheese. Top each with slightly overlapping banana slices. Cover with remaining bread to make sandwiches.
Melt 2 Tbsp. butter over medium heat in a large nonstick skillet. Meanwhile, in a large, shallow bowl, beat eggs, milk, vanilla and salt with a fork. Dip 4 sandwiches into egg mixture to soak both sides, about 5 seconds. Lay sandwiches in skillet and cook, turning until browned, about 5 minutes one side, 3 minutes other side. Repeat with remaining butter and sandwiches. When done, transfer to oven racks; do not stack. Serve hot with warm maple syrup.