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Have ready a large bowl of ice water. Place the eggs in a large pot, add water to cover by 1 inch, bring to a boil, uncovered, then immediately cover. Remove from the heat, let sit for 12 minutes, then transfer immediately to the ice water to cool for 5 minutes, and peel.
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Meanwhile, remove the crusts from the bread slices. In a food processor, process the bread into crumbs. In a skillet over medium heat, melt the butter. Add the garlic and breadcrumbs and stir frequently until the breadcrumbs are golden brown and crisp, 4 to 5 minutes. Set aside to cool.
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Halve the eggs lengthwise. Carefully remove the yolks and transfer them to a mixing bowl. Mash completely with a fork. Stir in the mayonnaise, sour cream, chives, parsley, thyme, mustard, lemon zest, and lemon juice until combined. Season with salt and pepper to taste. Using a small spoon, piping bag, or ziplock plastic bag with a corner snipped, fill the egg whites with the yolk mixture.
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Just before serving, sprinkle the deviled eggs with breadcrumbs, season with red pepper flakes, and serve.