Rinse the buckwheat thoroughly in a fine-mesh sieve, then combine with 0.5 cup water in a small pot.
Bring the buckwheat to a boil, then reduce heat to low, cover, and simmer for 10-12 minutes until water is absorbed and grains are tender.
While buckwheat cooks, pat the chicken livers dry with paper towels and season both sides with sea salt and black pepper.
Heat the olive oil in a stainless steel or cast iron skillet over medium-high heat.
Add the thinly sliced red onion to the skillet and sauté for 3-4 minutes until softened and slightly caramelized.
Push the onions to the side of the pan and add the chicken livers; sear for 2-3 minutes per side until browned but still slightly pink in the center.
Stir in the minced garlic and the black beans, tossing everything together for 1 minute to heat through.
Pour the balsamic vinegar into the pan to deglaze, using a wooden spoon to scrape up the flavorful browned bits from the bottom.
Fluff the cooked buckwheat with a fork and plate it as the base, topping with the chicken liver and bean mixture.
Garnish with freshly chopped parsley and serve immediately.