Cut the ahi tuna into bite size chunks, about a 1/2" cubes.
In a small bowl, mix together the spices and set aside.
Place a frying pan or cast iron skillet over high heat until it starts to smoke. Keep kitchen area well ventilated.
Toss the Ahi Tuna cubes in melted butter and then coat with spice mixture on both sides. Sear on high heat each side no more then 30 seconds, 1 minute to cook through well. Set aside.
In a large soup pot melt the butter and sauté the thinly sliced leek and diced shallot until light golden.
Sprinkle the leek and shallot with the flour to coat and cook on low for 2 minutes more. Slowly add the chicken stock and allow soup base to slightly thicken.
Chop the swiss chard, thinly chop the cabbage and cut broccoli into small florets. Add the vegetables to the pot and cook on medium heat for 8-10 minutes. Keep vegetables al dente.
Add the steamed rice and cooked barley with the tarragon and stir. Season with kosher salt and pepper to taste.
Ladle soup into bowls, top with blackened ahi tuna and serve.