In a large bowl, whisk together the marinade ingredients (ginger, garlic, lime zest, lime juice, soy sauce, fish sauce, brown sugar, neutral oil, and sriracha). Add the chicken thighs and toss to coat. Let marinate for at least 15 minutes while you start the broth.
In a large pot, melt the coconut oil over medium heat. Add the yellow curry paste and fry for 2-3 minutes, stirring frequently. Add the shallot, garlic, and ginger and stir to combine, then pour in the chicken stock. Bring to a gentle simmer and cook for 20-25 minutes.
Meanwhile, remove the chicken from the marinade, letting any excess drip off. Heat a skillet—I like cast iron here—over medium heat. Add the chicken and cook for about 5 minutes on the first side, then flip and cook for another 3 minutes, or until a golden char develops and the internal temperature reaches 165°F. Transfer to a cutting board/plate and let rest before slicing.
Strain the shallot, garlic, and ginger from the broth and discard. Shake the can of coconut milk well, then stir it into the broth. Cook over medium-low heat for 1-2 minutes, just until warmed through. Stir in the fish sauce and brown sugar, then remove from the heat and add lime juice to taste.
To assemble, divide the cooked rice between bowls and top with the sliced chicken thighs. Ladle the yellow curry broth over top, then finish with crispy shallots, fresh mint, lime wedges, and a drizzle of chili oil, if you like.