Start with the components that need chilling time. For the tzatziki sauce, grate the cucumber and squeeze it dry in a clean kitchen towel to remove excess moisture—this prevents a watery sauce. Combine the grated cucumber with Greek yogurt, minced garlic, dill, fresh mint, lemon juice, salt, and pepper in a bowl. Mix well and refrigerate while you prepare the rest of the dish. For the cucumber salad, dice the cucumber into 1/2-inch pieces, halve the cherry tomatoes lengthwise, and thinly slice the red onion. Toss these vegetables together with lemon juice, red wine vinegar, salt, and pepper. Set aside at room temperature.
In a large bowl, whisk together olive oil, lemon juice, oregano, dill, thyme, 3 tsp freshly minced garlic, salt, and pepper. Add the chicken chunks and toss thoroughly to coat every piece evenly with the marinade. I like to use fresh minced garlic rather than pre-minced because it releases more aromatic oils during marinating. Let the chicken marinate for 15-30 minutes at room temperature to allow the flavors to penetrate the meat.
While the chicken marinates, cook the quinoa according to package directions (typically 2 cups quinoa with 4 cups water, simmered for 15 minutes). Once cooked, fluff with a fork and set aside. Cooking the quinoa now ensures it's ready to serve when everything else comes together.
Heat a large skillet or grill pan over medium-high heat until very hot. Working in batches if necessary to avoid crowding the pan, sear the marinated chicken chunks for 5-8 minutes per side until golden brown and cooked through (internal temperature should reach 165°F). The high heat creates a flavorful crust while sealing in juices. Once cooked, transfer the chicken to a plate and let it rest for 5 minutes before slicing or serving.
While the chicken rests, warm the pita breads in a dry skillet or directly over a gas flame for about 30 seconds per side until warm and pliable, then cut into triangles. To assemble the bowls, divide the cooked quinoa from Step 3 among serving bowls. Top each bowl with the rested chicken, cucumber salad from Step 1, crumbled feta, warm pita triangles arranged on the side, and a generous dollop of chilled tzatziki sauce from Step 1. I like to drizzle the sauce over the top rather than keeping it on the side so every bite gets that cool, creamy element.