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 each pan and turn the heat to high. When the foam subsides, invert a pie pan of shrimp over the skillet so they fall into the pan all at once. Repeat with the other pan of shrimp. Cook the shrimp, undisturbed, 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 ginger, lime juice and zest, mint, and basil to each pan, and shake to combine.

Divide the shrimp among 4 plates or a serving platter and serve hot or at room temperature.