Whisk together the coconut milk, lime juice, lime zest, garlic, honey, soy sauce, cumin, smoked paprika, and black pepper.
Reserve 1/3 cup of the marinade in a clean container before adding the raw chicken.
Place the chicken in a shallow container or resealable bag and pour the remaining marinade over it.
Refrigerate for at least 30 minutes and up to 4 hours.
Prepare the jasmine rice according to package directions and fluff with a fork.
Slice the cucumber, prepare the carrots and avocado, and chop the cilantro and green onions.
Preheat a grill or grill pan to medium-high heat.
Remove the chicken from the marinade and discard all marinade that contacted the raw chicken.
Grill the chicken for approximately 5–7 minutes per side, depending on thickness, until the internal temperature reaches 165°F (74°C).
Transfer the chicken to a cutting board and rest for 5 minutes before slicing.
Whisk the safely reserved 1/3 cup marinade with 1 tablespoon fresh lime juice. Thin with 1–2 tablespoons water if necessary.
Divide the rice between four bowls.
Top with sliced grilled chicken, cucumber, carrots, and avocado.
Drizzle lightly with the coconut-lime sauce.
Finish with cilantro, green onions, and fresh lime wedges.
Serve immediately.