Add the cilantro, Thai basil, shallot, lemongrass (white part), fish sauce, oyster sauce, lime juice, maple syrup, brown sugar, chili paste, toasted sesame oil, ginger, garlic, ground turmeric, and Chinese five-spice to a high-powered blender. Blend until smooth, scraping down the sides as needed.
Place the pounded chicken in a large resealable freezer bag or a bowl and pour in the marinade. Turn to coat thoroughly, then seal or cover and refrigerate for 2 to 12 hours.
If grilling: preheat the grill to about 400°F (with the lid closed). Clean and oil the grates.
Grill the marinated chicken, undisturbed with the lid closed, 5–7 minutes per side until cooked through. For breasts, cook to 160°F; for thighs, cook to 170°F, then rest 5 minutes to reach final temp.
If using a skillet or grill pan: heat 1 tablespoon olive oil over medium-high until very hot. Add chicken and cook undisturbed 3–4 minutes until deeply golden. Flip, cover, reduce heat to medium, and cook 5–7 more minutes or until chicken reaches the temperatures above, then rest 5 minutes.
If baking breasts: preheat oven to 425°F and arrange chicken in a single layer in a lightly greased baking dish. Bake 14–16 minutes for small/medium (5–6 oz), 16–20 minutes for medium/large (7–9 oz), or 20–25 minutes for larger breasts until they reach 160°F, then rest 5 minutes.
If baking thighs: bake at 425°F in a lightly greased dish 25–30 minutes until thighs reach 170°F, then rest 5 minutes.
Serve the chicken with Asian sweet chili sauce, garnish with cilantro, sesame seeds, lime wedges, and cashews as desired.