In a large bowl or resealable plastic bag, whisk together the shallots, lemongrass, fish sauce, soy sauce, lime juice, brown sugar, Thai red curry paste, sweet chili sauce (if using), 1 tablespoon olive oil, minced garlic, grated ginger, red chili paste, and dried basil until smooth.
Add the pounded chicken thighs to the marinade and turn to coat evenly. Reserve 3 tablespoons of the marinade if using for noodle bowls.
Marinate the chicken for 30 minutes at room temperature or up to 24 hours in the refrigerator.
If refrigerated, let the chicken sit at room temperature 15–30 minutes before cooking.
To cook in a skillet: heat a large skillet over medium-high heat and work in batches if needed. Remove chicken from the marinade, letting excess drip off. Add chicken and cook undisturbed 3–4 minutes until browned, flip, cover, reduce heat to medium, and cook 3–5 more minutes until cooked through. Let rest 5 minutes before slicing.
To grill: grease and preheat the grill to medium (375–450°F). Remove chicken from the marinade and let excess drip off. Grill undisturbed 5–7 minutes per side, or until an instant-read thermometer reads 165°F. Let rest 5 minutes before slicing.
