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1
In a medium (3-quart) saucepan, heat 4 tablespoons butter over medium heat until foaming. Add shallots, sliced celery ribs, fennel bulb, garlic, scallion whites, and a generous pinch of salt. Cook, stirring occasionally, until vegetables are soft, have released all their liquid, and liquid has evaporated, about 10 minutes. Off heat, stir in absinthe. Transfer mixture to food processor bowl.
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2
Process vegetables, scraping down sides of food processor bowl as needed, into a coarse paste, about 30 seconds. Stop processor and add parsley, celery leaves, fennel fronds, and scallion greens to food processor bowl. Continue processing until herbs are broken down and well-combined with vegetable mixture, about 30 seconds. With food processor still running, gradually add remaining 4 tablespoons butter, making sure butter is emulsified into paste before adding more. Stop processor and add panko bread crumbs. Pulse mixture until bread crumbs are fully incorporated. Season to taste with salt, erring on the side of less salt, since the oysters are briny. Transfer mixture to disposable pastry bag or small mixing bowl, and set aside. If using a mixing bowl, cover with plastic wrap, pressing plastic against surface of the paste to prevent skin from forming. If not serving immediately, mixture can be stored in refrigerator for up to 1 day; let sit at room temperature to soften before using, about 30 minutes.
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3
Adjust oven rack to 6 inches below the broiler element and preheat the broiler on high. Line rimmed baking sheet with an even 1/2-inch layer of rock salt.
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4
and arrange them on prepared baking sheet. Pipe or spoon butter topping over oysters, and then use an offset spatula or butter knife to smooth topping and fully cover each oyster.
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5
Broil oysters, checking them frequently, until topping begins to brown and oysters are warmed through, 4 to 6 minutes. Serve immediately, passing lemon wedges at the table.
