In a large bowl or Ziploc bag, whisk together the marinade ingredients: olive oil, minced shallots, chopped lemongrass, fish sauce, soy sauce, lime juice, brown sugar, Thai red curry paste, sweet chili sauce, minced garlic, grated ginger, red chili paste, and dried basil. Reserve 3 tablespoons of this marinade if you plan to make Vietnamese noodle bowls.
Add the chicken thighs to the marinade and ensure each piece is evenly coated. Marinate for 30 minutes at room temperature, or for up to 24 hours in the refrigerator for deeper flavor.
If marinated chicken has been refrigerated, allow it to sit at room temperature for 15 to 30 minutes before cooking to ensure even cooking.
Heat a large skillet over medium-high heat. You may need to work in batches, so don't overcrowd the pan. Remove the chicken from the marinade, letting the excess drip off, and add the chicken to the skillet.
Cook undisturbed for 3 to 4 minutes, or until the first side is nicely browned. Turning the chicken over, cover, and reduce the heat to medium. Cook for an additional 3 to 5 minutes, depending on the thickness, until the chicken is cooked through with an internal temperature of 165 degrees Fahrenheit.
Let the chicken rest for 5 minutes before slicing into pieces. This resting time allows the juices to redistribute, ensuring tender bites.
For grilling, preheat the grill to medium heat (375 to 450 degrees Fahrenheit). Remove the chicken from the marinade, letting excess marinade drip off. Grill the chicken undisturbed for 5 to 7 minutes per side, or until cooked through.
After grilling, let the chicken rest for 5 minutes to enhance flavors and moisture retention before slicing.