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Preheat the oven to 375°F with a rack in the lowest position. Place a non-greased, rimmed baking sheet onto the rack.
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To make the compote: In a small pot, combine the raspberries, sugar, and lemon juice. Cook the mixture over medium heat, stirring often to prevent burning. As the berries soften, press on them with the back of a spoon or spatula until they’re completely broken down and the mixture is bubbling rapidly. Once the mixture boils, turn down the heat to a simmer.
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Continue to cook over low heat until a spoon or spatula leaves a clean path when swiped across the bottom of the pot that disappears after 2 to 3 seconds; this will happen after about 10 to 15 minutes of cooking.
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Remove the compote from the heat and stir in the lemon zest. Set aside while you prepare the French toast.
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To make the French toast: Slice six 3/4"-thick slices of bread from the loaf of your choice.
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In a medium bowl, whisk the milk, buttermilk, vanilla, nutmeg, and 1/8 teaspoon of the salt until combined. Pour the mixture into an 8" square or round pan. A shallow bowl or dish with at least a 2-cup capacity will also work.
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In the same bowl (no need to clean it first), whisk together the eggs, brown sugar, and remaining 1/8 teaspoon salt until slightly frothy and fully combined. Transfer the egg mixture to another 8" square or round pan, or simply leave it in the bowl.
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Carefully, remove the hot baking sheet from the oven and place it on a cooling rack. Add the cubed butter to the hot baking sheet; return to the oven for 1 to 2 minutes to completely melt the butter. Use a pastry brush or tilt the baking sheet to create a thin, even layer of butter across the entire surface of the baking sheet.
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Arrange the bread slices, dish of milk, dish of eggs, and buttered baking sheet in a line, from left to right. Starting with the bread, work your way to the right by placing a slice into the milk mixture for 5 seconds, then flip and let soak for an additional 5 seconds.
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Remove the slice from the milk mixture and allow any excess to drip back into the dish before placing the slice of bread in the egg mixture. Allow to soak for 2 seconds, then flip and soak for an additional 2 seconds. Rotate once more so each side is coated twice. Lift up and allow any excess egg to drip back into the dish before carefully placing the slice onto the prepared baking sheet.
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Repeat this process with the remaining slices of bread.
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Bake the sheet pan French toast for 15 to 20 minutes. Use a small offset spatula or fork to lift the edge of one piece and check the bottom of the bread; it should be golden brown with darker caramelized edges.
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Remove the pan from the oven and carefully flip each piece over. Return to the oven and bake for 5 to 10 more minutes. The toast should be fragrant, evenly colored on both sides, and slightly puffed in the middle.
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Remove the pan from the oven, allowing the French toast to cool for 5 minutes before transferring to plates for serving.
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Serve the French toast bake warm, topped with raspberry-lemon compote, maple syrup, or a dusting of confectioners’ sugar.
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Storage information: Refrigerate any leftover French toast bake in an airtight container, in a single layer for several days; freeze for longer storage. Reheat in preheated 350°F oven for 10 to 15 minutes, or until warm.