In a shallow baking dish, arrange the bread slices in a single layer. In a bowl, combine the eggs, milk, vanilla, cinnamon and brown sugar and whisk until blended. Pour the mixture over the bread and let stand for 2-3 minutes so the bread can absorb the liquid. Turn the slices over and let the bread absorb the remaining liquid, 2-3 minutes more.

Preheat a large skillet and coat generously with butter. When the skillet is hot, cook the bread in batches (do not overcrowd) until golden and crisp, 3 to 4 minutes per side.