Heat the broiler to high and place a rack in the center of the oven.
Whisk together the eggs, mascarpone, basil, tarragon, chile paste, lemon zest and 1/2 teaspoon salt in a medium bowl. Set aside.
Heat a medium (10-inch) nonstick ovenproof saute pan over medium heat. Add the oil and heat another minute. Add the artichoke hearts and cook, stirring often, until warmed through, about 2 minutes. Add the spinach and remaining 1/2 teaspoon salt. Cook, stirring occasionally, until the spinach is wilted, about 2 minutes longer. Add the crab and stir to combine. Add the egg mixture and allow to sit for 1 minute. Using a rubber spatula, stir the cooked egg mixture up from the bottom and sides, allowing the raw mixture to begin to cook. Continue to do this until the mixture is beginning to look like a soft scramble, about 4 minutes. Spread the mixture evenly on top and place under the broiler until the mixture is completely set and the top is golden brown, 3 to 4 minutes. Allow to cool for 5 minutes before slicing and serving warm.