Step 1

Whisk garlic, lime juice, fish sauce, cayenne, brown sugar, garlic powder, red pepper flakes, dried thyme, allspice, onion powder, black pepper, paprika, cinnamon, nutmeg, and 3 Tbsp. oil in a large bowl. Add chicken, season generously with salt, and turn several times to coat. Let sit, turning chicken pieces once, at least 2 hours, or cover and chill up to 1 day.

Step 2

Prepare grill for medium-high, indirect heat (for a charcoal grill, bank coals on one side of grill; for a gas grill, turn one or two burners to medium-low). Lightly brush grate with oil. Arrange chicken thighs, skin side down, on grate over hottest part of grill and grill, turning halfway through, until lightly charred, 5–10 minutes. Move chicken to cooler part of grill and continue to grill, turning several times, until an instant-read thermometer inserted into the thickest part registers 165°, 20–25 minutes longer. Transfer chicken to a platter and let rest 10 minutes.

Step 3

Top chicken with banana peppers and cilantro and serve with lime wedges for squeezing over.