Preheat oven to 250 degrees. Line a baking sheet with foil and place in the oven to warm.
Whisk together the eggs, half and half and vanilla in an 8-inch square baking dish until combined. Whisk in 2 tablespoons of the brown sugar, the cinnamon, nutmeg and salt.
Melt 1 tablespoon of the butter in a large nonstick skillet over medium heat. Meanwhile, dip 4 slices of banana bread very briefly in the egg mixture (don't soak) letting the excess drip back in the dish. Add the dipped banana bread to the skillet and sprinkle each slice with 1 tablespoon brown sugar and pat in. Cook until the underside is golden brown, about 2 minutes. Flip and cook until golden brown on the second side, about 2 minutes. Put on the baking sheet in the oven to keep warm and repeat with the remaining banana bread, batter, adding 1 tablespoon more butter to the skillet and sprinkling the slices with 1 more tablespoon brown sugar. Keep the second batch of French toast in the oven.
Wipe the skillet clean with a paper towel and add the remaining 2 tablespoons butter. Once the butter melts, add the remaining 2 tablespoons brown sugar and the lemon juice and stir until smooth. Add the bananas and toss until glazed, about 1 minute. Serve the French toast topped with the bananas and chopped walnuts.
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