Melt 2 tablespoons butter in a medium saucepan over high heat. Add the onion, sliced jalapeno and thyme and cook, stirring, until softened, 2 to 3 minutes. Add the garlic and ginger and cook, stirring, until golden, about 1 minute. Add 2 more tablespoons butter and the curry powder; cook, stirring, until the butter is melted and the curry powder is toasted, 30 seconds. Add the sweet potatoes and stir to coat, then add 1 teaspoon salt, a few grinds of pepper and 2 cups water. Bring to a boil, then reduce the heat to a simmer; cover and cook until the sweet potatoes are tender, about 15 minutes.
Add the chicken to the pan. Cut the remaining 2 tablespoons butter into pieces and stir into the mixture. Cook until the chicken is hot and the potatoes start falling apart, about 3 minutes. Season with salt and pepper.
Heat the lavash in a large nonstick skillet over high heat, about 30 seconds per side. Pile the chicken mixture in the center of each lavash; top with the cilantro and minced jalapeno. Fold in the sides and roll up like a burrito; cut in half.