In a small saucepan, combine the buckwheat groats and coarse salt with 1 cup (240 ml) of water. Bring to a boil, then reduce the heat to medium-low and cook for 10 to 15 minutes, until the groats are tender. Drain, rinse under cold water, and drain again.
While the groats cook, season the chicken breasts with salt and pepper. In a small bowl, mix the paprika, garlic powder, oregano, and 2 tablespoons oil until well combined. Brush the chicken breasts with this marinade on both sides.
In a medium dry skillet (without any oil), toast the pine nuts over medium heat for about 5 minutes, or until golden brown, stirring continuously to avoid burning. Remove them from the pan.
In the same skillet, heat a drizzle of oil over medium-high heat. Sear the chicken breasts for 4 to 5 minutes per side, until well browned. Reduce the heat to medium-low and continue cooking until the internal temperature of the chicken reaches 165°F (74°C). Transfer the chicken breasts to a cutting board and slice against the grain using a sharp knife.
In a large salad bowl, combine the cooked buckwheat, cherry tomatoes, cucumber, and arugula. Add the pesto and mix well. Divide the salad between two plates, top with slices of grilled chicken, and finish with some toasted pine nuts and a drizzle of oil. Serve immediately.