Preheat the oven to 350 degrees F.
Put the peaches, 2 tablespoons of the butter, 2 tablespoons of the maple syrup and the vanilla in a 2-quart oval baking dish. Toss with a spatula to combine, then arrange the peaches cut side up.
Put the bread and salt in the bowl of a food processor. Pulse until you have small crumbs (take care not to over-process or the crumbs can get gummy). Transfer to a medium bowl and mix with the remaining 2 tablespoons butter and 2 tablespoons maple syrup. Sprinkle the bread mixture evenly over the peaches.
Bake until the peaches are very tender and the bread crumbs are golden-brown, 30 to 35 minutes.
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