Directions

1. Combine feta, garlic, 2 tablespoons yogurt, 1 tablespoon oil and 1 teaspoon lemon juice in a food processor; process until very smooth, about 1 minute, stopping to scrape down the sides of the bowl once or twice.
2. With the processor running, slowly stream in 2 teaspoons water through the chute; process until the mixture appears whipped, about 2 minutes, stopping to scrape down the sides of the bowl as needed. Add the remaining 2 tablespoons yogurt; pulse until incorporated, about 3 (1-second) pulses. Transfer the whipped feta to a medium bowl; cover and refrigerate until ready to use.
3. Place flour in a shallow dish and place panko in a separate shallow dish. Crack egg into a third shallow dish. Add 1 tablespoon pesto and 1 tablespoon water to the egg; whisk until combined. Working with 1 cutlet at a time, dredge in flour, turning to coat. Place the floured cutlet in the egg mixture; turn to coat, letting excess drip back into the dish. Place the cutlet in the panko; turn to coat, patting lightly to adhere. Place on a large plate. Repeat with the remaining cutlets.(Discard any remaining egg mixture, flour and panko.)
4. Heat 1 1/2 tablespoons oil in a large skillet over medium heat. Add 2 breaded cutlets; cook, flipping once, until golden brown and crispy on both sides and an instant-read thermometer inserted into the thickest part registers 165°F, 4 to 6 minutes. (Reduce heat to medium-low as needed to prevent burning.) Transfer the cutlets to a clean plate; cover loosely with foil to keep warm. Repeat with another 1 1/2 tablespoons oil and the remaining 2 cutlets. Sprinkle the chicken with 1/8 teaspoon salt.
5. Wipe the skillet clean; heat the remaining 1 1/2 teaspoons oil over medium-high heat. Add tomatoes; cook, stirring occasionally, until starting to blister, about 5 minutes. Remove from heat; stir in pepper and the remaining 1 teaspoon lemon juice and 1/8 teaspoon salt.
6. Spread the whipped feta on a platter; sprinkle with Aleppo pepper, if desired. Arrange the chicken cutlets on top. Spoon the burst tomatoes over the chicken. Stir the remaining 2 tablespoons pesto and 1 tablespoon water together in a small bowl. Drizzle over the chicken.