Bring pomegranate juice to a simmer in a small pot over low heat, then let cook until very syrupy, thick and reduced to about 1/2 cup, 30 to 40 minutes. Set aside to cool.
Meanwhile, preheat oven to 300 degrees F.
Sprinkle chicken breasts liberally with kosher salt and pepper on both sides. Add oil to a medium ovenproof skillet and heat over medium-high heat. Place the chicken in the skillet skin-side down and cook until the skin is nice and golden brown, 2 to 3 minutes. Flip and cook for another 2 minutes. Transfer skillet to the oven and roast until the internal temperature reaches 165 degrees F, 10 to 12 minutes. Let rest for 5 minutes.
Slice the cooked chicken breast 1/4-inch-thick. Layer tomatoes, chicken and mozzarella in an elegant row on a long platter. Drizzle with pomegranate reduction, sprinkle with crushed pistachios, scatter basil leaves around and sprinkle with some smoked sea salt.