On a cutting board, lay your skirt steak longwise and cut into three inch segments, then cut each segment thinly against the grain. 

In a medium bowl, combine the steak, 1 teaspoon melted coconut oil, the arrowroot, 1 teaspoon of the salt, and the black pepper. Toss to coat thoroughly. Set aside for 5 minutes.

Heat a large sauté pan over high heat. When hot, reduce to medium-high and melt 1 tablespoon of the coconut oil in the pan. Add half the steak and cook until seared, about 2 minutes. Flip and cook until browned, about 30 seconds. Transfer the steak to a large plate and set aside. Carefully wipe out the pan with a paper towel, then add 1 tablespoon of the coconut oil and repeat with the remaining steak. Set aside with the other cooked steak.

Wipe out the pan and return it to medium-high heat. Melt the remaining 2 tablespoons coconut oil in the pan. When the oil is hot, reduce the heat to medium, add the shallots, and cook, stirring, until beginning to brown, about 30 seconds. Add the bell peppers, scallions, Thai chiles, and remaining ½ teaspoon salt and cook, stirring, until the bell peppers begin to soften, about 1 minute. Add the green beans and cook, stirring well, until warmed through, about 1 minute more. Add the peperoncini and garlic and cook, stirring, for 30 seconds.

Return the beef to the pan, along with any juices collected on the plate, and add the coconut aminos and the peperoncini brine. Stir to combine, then reduce the heat to medium-low. Add the basil, stir again, and turn off the heat. Serve.