Heat the 1/2 cup oil in a small saucepan over medium heat. Add the garlic and sauté until just starting to brown, about 2 minutes. Remove and discard garlic. Transfer the saucepan to a cooling rack and let oil cool to room temperature.
Add the cooled oil to a food processor or blender, along with the 1/2 cup scallions, parsley, cilantro, paprika, cumin, salt, turmeric and cayenne (if using). Process or blend until smooth.
Rub the mixture on both sides of the chicken breasts and let marinate 30 minutes.
Heat grill to medium heat. Grill chicken breasts until they have reached an internal temperature of 165 degrees F, about 5 to 7 minutes a side. (Discard the leftover marinade.)
While chicken is cooking, prepare the rice: In a large saucepan, heat the 1 tablespoon oil over medium heat. Add the 1 clove garlic and sauté until just starting to brown, about 2 minutes. Remove and discard garlic.
Add the rice, chicken broth or stock, the 1/4 cup scallions, salt and pepper to the pan and bring to a boil. Reduce heat, cover and simmer 5 minutes or until liquid is absorbed. Remove from heat and let sit covered for 5 minutes. Fluff with a fork and serve with the grilled chicken breasts.