In a large bowl, combine the oil, fish sauce, lime zest, lime juice, garlic, and salt. Add the chicken and toss well to coat. Cover and refrigerate for 1-2 hours.
Heat oil in a large Dutch oven or heavy bottomed pan, over medium-high heat. Sear chicken, 2-3 minutes per side, or until golden. Transfer the chicken to a plate and set aside.
In the same pan, over medium-low heat, add the sweet potato and cook for 3-4 minutes. Add the onions and red peppers and continue to cook for an additional 3-4 minutes. Stir in the chili, garlic, and ginger and season with salt and pepper. Add red curry paste and stir to combine. Stir in the coconut milk, chicken stock, and lemongrass. Add the chicken back to the pan, along with the spinach, carrots, and a squeeze of fresh lime juice. Remove from the heat.
To assemble phyllo topping, unroll the phyllo dough and scrunch each sheet into a bundle. Tuck them into the filling to cover the whole pan. Continue until all sheets are tucked in. Gently brush the melted butter over the phyllo dough and sprinkle with flaky salt. Transfer the pan to the oven on the middle rack, and bake for 15-20 minutes or until phyllo dough is browned all over.
Remove the pan from the oven, let rest for 10 minutes before serving. Top with fresh cilantro and spoon each portion into a bow. Enjoy!
