Heat the oven to 375 degrees. Generously grease the bottom of a 9-by-13-inch baking pan with butter.
In a wide, shallow bowl or dish, whisk together the milk, eggs, ¼ cup sugar and a pinch of salt until the sugar is dissolved. Immerse a piece of bread in the mixture, pushing it down until liquid pools on top and pausing to make sure the bread is well saturated. Transfer the slice into the baking pan, then repeat with the remaining slices. Spoon the remaining liquid over the top of the slices, stopping when the bread no longer immediately absorbs it. (Thinner pieces of smaller sandwich bread can hold less liquid than thicker pieces of wider rustic bread.)
Combine the remaining 2 tablespoons sugar with the cinnamon and sprinkle about half of the cinnamon sugar over the bread.
Bake until the custard is almost set and the edges of the bread are lightly golden and crispy, about 20 minutes. If desired, broil until even more golden on top, 1 to 2 minutes.
Remove from the oven and divide among plates, using a knife to slice apart the pieces if they’ve slightly fused together. Top each with a slice of butter, if desired, and serve with maple syrup, for drizzling, and the remaining cinnamon sugar to sprinkle on top.
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