Make the tomato salad: Slice the cherry tomatoes into quarters and add to a bowl with the fresh minced garlic, chopped basil, sherry vinegar, olive oil, salt and pepper. Let sit until ready to serve, ideally at least 20 minutes before.
Make whipped feta: In a food processor, combine the feta, basil, Greek yogurt and lemon zest. Blend, and while the processor is running, drizzle olive oil through the top opening, until the feta is whipped to a smooth mixture. Season to taste.
Pound the chicken: Place the chicken cutlets between two pieces of parchment paper or plastic wrap and use a meat mallet or rolling pin to gently pound them to about ¼-inch thickness.
Set up the breading station: Add flour to one shallow bowl, beaten eggs to a second, and breadcrumbs to a third, seasoning each with salt and pepper. Working one at a time, coat each cutlet in flour and shake off the excess, dip it into the egg, then press it into the breadcrumbs until evenly coated.
Fry the chicken: Add about ¼ inch of neutral or olive oil to a large skillet and heat over medium-high until the oil is hot and shimmering (350 degrees). Add the cutlets without overcrowding the pan and cook for about 2–3 minutes per side, until golden brown, crisp, and cooked through to 165°F.
Drain and season: Transfer the fried cutlets to a wire rack or paper towel-lined plate and immediately season with a pinch of salt.
Assemble: Add a few spoonfuls of feta to a shallow bowl. Add cutlet overtop and spoon over the tomato salad. Serve and enjoy!