Preheat an oven to 350 degrees F. Pat the chicken thighs very dry with paper towels and season all over with salt and pepper.
Heat the oil in a large cast-iron or oven-safe skillet over medium-high until shimmering. Working in batches if needed, add the chicken skin-side down and cook until the fat is rendered and the skin is golden-brown, 8 to 10 minutes. Transfer the chicken to a plate, skin side up. Pour out the rendered fat, except for 1 tablespoon, and let the pan cool slightly.
Return the pan to medium heat and add the sliced shallot, garlic, ginger, and serranos and cook for 2-3 minutes while stirring often until soft. Add the curry paste and cook for another minute or two while stirring, until the curry paste is very fragrant. Then, add the coconut milk and scrape up any bits from the bottom of the pan while bringing the sauce to a simmer. Add the brown sugar, fish sauce, and cornstarch slurry and simmer the sauce for another 2 minutes. Season to taste with salt and pepper to taste.
Arrange the cubed potatoes in the pan and stir so that they're coated with the sauce. Gently nestle the chicken back into the pan, skin-side up, in a single layer taking care to ensure that the skin isn't submerged. Transfer the whole skillet to the oven uncovered and bake for 1 hour, or until the potatoes are very tender. Remove the skillet from the oven.
Before serving, top with cilantro, lime, and sliced serranos. Serve over steamed rice.