In a medium bowl, combine minced garlic, soy sauce, olive oil, brown sugar, cumin, paprika, black pepper, and salt. Whisk until well blended.
Place the chicken thighs in a resealable plastic bag or shallow dish and pour the marinade over the chicken. Seal the bag or cover the dish and refrigerate for at least 30 minutes, or up to 2 hours for more flavor.
Preheat the grill or a skillet over medium-high heat. Remove the chicken from the marinade, allowing excess to drip off.
Grill or cook the chicken for about 6-7 minutes per side, or until the internal temperature reaches 165°F and the chicken is nicely browned.
While the chicken is cooking, melt butter in a large skillet over medium heat. Add the sliced zucchini and sauté for about 5-7 minutes, or until tender and slightly golden. Season with salt and pepper to taste.
Once the chicken is cooked, let it rest for a few minutes before slicing. Serve the chicken alongside the sautéed zucchini and garnish with fresh parsley.