Divide the shrimp between two 8- or 9-inch pie pans and pat them completely dry with a paper towel. Arrange the shrimp so they lay flat and are evenly spaced in the pans.
Heat 2 large skillets over medium heat. Season the shrimp with salt and pepper; add a teaspoon of butter to one of the pans and turn the heat to high. When the foam subsides, invert a pan of shrimp over the skillet so they fall into the pan all at once. Repeat with the other shrimp. Cook the shrimp, without moving them, until they turn golden brown on the bottom, about 2 minutes. Add a remaining teaspoon of butter to each pan and turn off the heat. Turn the shrimp over with tongs and cook for 1 minute in the residual heat of the pans. Add half the zest, juice, and dill to each pan, and shake the pan to combine.
Divide the shrimp among 4 plates or arrange on a platter. Serve hot or at room temperature.
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