Combine 1 tablespoon olive oil, 1 tablespoon lime juice, 2 teaspoons minced garlic, smoked paprika, 1 teaspoon sugar, cumin, 1/4 teaspoon salt, and 1/4 teaspoon pepper in a large zip-top plastic bag. Add chicken to bag; seal bag. Let stand 15 minutes, turning occasionally.
Preheat grill to medium.
Coat grill rack with cooking spray. Remove chicken from marinade; discard marinade. Sprinkle chicken with 1/4 teaspoon salt and 1/4 teaspoon pepper. Add chicken to grill rack; grill 8 minutes on each side or until done.
Place remaining 2 tablespoons oil, remaining 1 tablespoon juice, remaining 1 teaspoon garlic, remaining 1/2 teaspoon sugar, remaining 1/4 teaspoon salt, remaining 1/4 teaspoon pepper, parsley, half-and-half, and jalapeño in the bowl of a mini food processor; process until finely chopped. Serve sauce with chicken thighs.