Preheat the oven to 375℉.
In a medium bowl or jar, combine the braising liquid ingredients and whisk until very well combined. Set aside.
Pat dry the chicken leg quarters and season with salt and pepper.
In a large braiser or oven safe skillet, heat the oil over medium-high heat. Arrange the chicken, skin side down, in a single layer in the pan and cook until a deep golden-brown crust forms, 6 to 8 minutes.
Remove from the heat and flip the chicken so that it is skin side up and arranged in a single layer in the pan. Scatter the shallots, ginger, scallions and Thai chiles over and around the chicken pieces. Pour the braising liquid around and over the chicken.
Transfer to the oven, uncovered, and cook until cooked through and fork tender, about 1 hour.
Remove from the oven and let rest for 10 minutes to let the juices settle. Garnish with the fresh Thai basil and cilantro. To serve, place some steamed rice in the bottom of a shallow bowl and top with a chicken quarter. Ladle the broth over the top and around the chicken (you want it extra brothy). Enjoy!