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1
Process 1/2 cup pecans, 1 tablespoon light brown sugar, and 1/4 teaspoon cinnamon in food processor until coarsely ground, 12 to 15 one-second pulses (you should have about 1/2 cup crumbs).
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2
Adjust oven rack to middle position and heat oven to 300 degrees. Place bread on wire rack set in rimmed baking sheet. Bake bread until almost dry throughout (center should remain slightly moist), about 16 minutes, flipping slices halfway through cooking. Remove bread from rack and let cool 5 minutes. Return baking sheet with wire rack to oven and reduce temperature to 200 degrees.
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3
Whisk milk, yolks, sugar, cinnamon, 2 tablespoons melted butter, salt, vanilla, and rum in large bowl until well blended. Transfer mixture to 13- by 9-inch baking pan.
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4
Soak bread in milk mixture until saturated but not falling apart, 20 seconds per side. Using firm slotted spatula, pick up bread slice and allow excess milk mixture to drip off; repeat with remaining slices. Place soaked bread on another baking sheet or platter. Sprinkle each slice of soaked bread with 1 tablespoon nut mixture.
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5
Heat 1/2 tablespoon butter in 12-inch skillet over medium-low heat. When foaming subsides, use slotted spatula to transfer 2 slices soaked bread to skillet-nut mixture side down-and cook until golden brown, 3 to 4 minutes. Flip and continue to cook until second side is golden brown, 3 to 4 minutes longer. (If toast is cooking too quickly, reduce temperature slightly.) Transfer to baking sheet in oven. Wipe out skillet with paper towels. Repeat cooking with remaining bread, 2 pieces at a time, adding 1/2 tablespoon of butter for each batch. Serve warm, passing maple syrup separately.
