Dry the artichokes, cut in half lengthwise, and slice lengthwise about 1/2 inch thick.
Heat 2 Tbs. of the olive oil in a 10-inch nonstick skillet over medium heat. Add the artichokes, a pinch of salt, and a couple of grinds of pepper. Cook the artichokes until lightly browned on one side, about 4 minutes. With a wide spatula, turn them over and cook until lightly browned on the other side, about 1 minute. Add 1/4 cup water and bring to a boil. Reduce the heat to low, cover, and simmer until tender, about 4 minutes. Remove the cover and cook until any remaining liquid is evaporated. Transfer to a small bowl.
Add 2 Tbs. of the oil and the leeks to the pan with a pinch of salt. Increase the heat to medium low and cook, stirring occasionally, until soft and tender, 10 to 12 minutes. Transfer to the bowl with the artichokes.
Whisk the eggs in a medium bowl. Add the artichokes, leeks, Taleggio, parsley, thyme, and 1/2 tsp. salt.
Position an oven rack 6 inches from the broiler and heat the broiler on high. Wipe out the skillet and heat the remaining 1 Tbs. oil over medium-low heat. Pour in the egg mixture and cook until the bottom is light golden (use a spatula to peek), about 4 minutes. Slide the spatula under the bottom to keep it from sticking. Put the pan under the broiler and cook until the eggs are set and the top is golden-brown, about 3 minutes more. Slide onto a serving platter and serve warm or at room temperature.
nutrition information (per serving):
Photo: Scott Phillips