Combine the dried oregano, chili powder, ground coriander, ground cumin, grated garlic, grated shallot, lime zest, lime juice, honey, coarse salt, and black pepper in a medium bowl.
Whisk the mixture while slowly drizzling in the oil until the marinade is emulsified and uniform.
Alternatively, place all ingredients except the oil in a blender and blend on high; if blending, use only 2 garlic cloves and 1/4 of the shallot to avoid overpowering the marinade, then add the oil and blend briefly to emulsify.
Add the chicken to the bowl (or transfer the marinade to a resealable bag) and thoroughly coat the pieces with the marinade.
Refrigerate and marinate the chicken for at least 2 hours and up to 24 hours for best flavor; do not exceed 48 hours.
To pan-sear: heat 1–2 tablespoons oil in a nonstick skillet over medium-high heat. Cook chicken about 6–7 minutes per side, adjusting heat to avoid burning, until internal temperature reaches 165°F for white meat or 175°F for dark meat. Rest 3–4 minutes before serving.
To grill: preheat grill to medium-high (about 325–350°F). Grill chicken 6–7 minutes per side with the lid closed, rotating 90° halfway through a side for grill marks, until internal temperature reaches the same targets. Rest 3–4 minutes before serving.