In a medium non-reactive bowl, whisk together lime juice, olive oil, minced garlic, cumin, smoked paprika, chipotle (or adobo), honey, salt, pepper, ¼ cup of the diced red onion, and cilantro stems until fully emulsified.
Place chicken in a large resealable plastic bag or shallow dish. Pour marinade over chicken, ensuring all pieces are coated. Seal or cover and refrigerate for at least 30 minutes or up to 12 hours (for thighs) or 4 hours (for breasts).
Remove chicken from refrigerator 15–20 minutes before cooking. Discard used marinade. Pat chicken very dry with paper towels.
Heat grill or heavy skillet (cast iron preferred) over medium-high heat until hot. Lightly oil grates or pan.
Place chicken on hot surface. Grill or sear undisturbed for 5–6 minutes until deeply browned and easily releases. Flip and cook another 4–7 minutes, until internal temperature reaches 160°F for breasts or 175°F for thighs.
Transfer chicken to a cutting board, tent loosely with foil, and rest for 8–10 minutes.
While chicken rests, halve and pit avocados. Scoop flesh into a bowl and mash with a fork to desired consistency. Stir in juice of 1 lime, remaining ¼ cup diced red onion, 2 tablespoons chopped cilantro leaves, and ¼ teaspoon salt. Adjust seasoning.
Slice rested chicken against the grain into ½-inch strips.
Arrange chicken on plates or in bowls. Top generously with avocado mixture. Sprinkle with queso fresco, additional cilantro leaves, and lime wedges. Add optional toppings as desired.
Serve immediately — best enjoyed fresh and vibrant.