Preheat the oven to 400°F (200°C).
In a mixing bowl combine 2 tablespoons of the olive oil, tomato paste, smoked paprika, chopped garlic, lemon zest, chili flakes, and a generous pinch of salt and pepper; toss to make a coating for the chicken.
Pat the chicken dry and toss with the seasoning mixture until evenly coated.
Heat the large oven-safe skillet over medium-high heat and add the remaining 1 tablespoon olive oil. Sear the chicken on both sides until golden, about 3–5 minutes per side.
During the last 2 minutes of searing, add the butter to the skillet. Then remove the chicken to a plate, leaving the skillet over the heat.
Add the orzo and fresh thyme to the hot skillet and cook, stirring, until the orzo is lightly toasted, about 1 minute.
Stir in the chopped sun-dried tomatoes, chicken broth, and the 2 tablespoons lemon juice; season with salt and pepper. Mix in the mixed fresh herbs.
Return the seared chicken and any collected juices to the skillet, nestling the pieces into the orzo mixture.
Bake the skillet uncovered in the preheated oven for about 15 minutes, or until the chicken is cooked through and the orzo is tender.
Spoon tzatziki sauce over the chicken and orzo before serving and garnish with extra basil if desired.