To caramelize the leeks, cut the leeks in half and soak to clean them. Melt butter in large nonstick skillet over medium heat. Add leeks and stir to coat. Add a splash of wine. Cover and cook until leeks are golden brown, stirring every 5 minutes, about 20 minutes total. Season to taste with salt and pepper.
To prepare the scallops and vegetables, heat one teaspoon of the olive oil in a sauté pan on high heat. Let the pan get really hot, but not too hot. You want the oil to dance and shimmer, but not smoke. Salt the scallops. Sear scallops—until the bottoms form a nice brown crust—then add a little (½ teaspoon) butter to the pan. Turn scallops over. Lower heat, cook through, basting with the butter.
In second pan, heat one teaspoon of olive oil. Sweat the shallots. Sweating is simmering over low heat in butter or oil, covered, without browning. Add pepper. Cook until shallots soften. Add corn kernels and leeks. Salt as you go—don’t overdo the salt. Taste. Don’t cook without tasting! Add a splash of wine (about two tablespoons) and a little more salt and pepper if needed. Add arugula and basil, sir briefly and turn off heat.
Mound vegetables on a plate, placing leeks on top, then position scallops on plate. Make a quick sauce from the scallops’ cooking juices: add a little wine and butter to the pan, swirl. Dribble sauce over scallops on plate.