In a large bowl, whisk together the 3 tbsp extra virgin olive oil, red wine vinegar, lemon zest, oregano, paprika, garlic powder, sea salt, and black pepper. Add the chicken breasts and turn to coat them thoroughly. Set aside to marinate at room temperature for at least 20 minutes while you prepare the other components.
Preheat your oven to 400°F (200°C). On a baking sheet, toss the dried chickpeas with 1 tbsp olive oil, smoked paprika, and cumin until evenly coated. Spread into a single layer and roast for 20-25 minutes, shaking the pan halfway through, until they are golden and crisp.
While the chickpeas roast, cook the farro. In a medium saucepan, bring 4 ½ cups of water to a boil. Add the farro, reduce the heat to a simmer, cover, and cook until the grains are tender yet chewy, about 20-25 minutes. Drain any excess liquid and set aside.
To prepare the tzatziki, grate the unpeeled cucumber onto a clean kitchen towel. Gather the corners and squeeze firmly over the sink to remove as much moisture as possible—this is key to a thick sauce. In a medium bowl, combine the squeezed cucumber, Greek yogurt, minced garlic, lemon juice, chopped dill, and 1 tbsp olive oil. Stir until smooth and chill until ready to serve.
Heat a large cast-iron skillet or grill pan over medium-high heat. Once hot, place the chicken breasts in the pan, ensuring they don't overcrowd it. Cook for 6-8 minutes per side, until golden brown and an instant-read thermometer inserted into the thickest part registers 165°F (74°C). Transfer the chicken to a cutting board and let it rest for 5-10 minutes before slicing into bite-sized pieces.
Assemble the six bowls. Create a foundation with a generous portion of chopped romaine and about ¾ cup of cooked farro. Arrange the sliced chicken, roasted chickpeas, cherry tomatoes, red bell pepper, and red onion over the top. Finish with a sprinkle of crumbled feta and a generous dollop of the herb-infused tzatziki.