Smash the garlic cloves, sprinkle with 2 teaspoons kosher salt, and, with the flat side of a large knife, mash and smear the mixture into a coarse paste. Transfer to a lidded storage container. Add 1/2 teaspoon pepper and the lemon zest. Whisk in 1/4 cup of the lemon juice and 1/3 cup of the olive oil. Add the chicken cutlets; toss to coat. Cover and refrigerate 1 hour or up to overnight.
Heat a heavy grill pan over medium-high heat. Working in batches, cook the chicken cutlets until charred and cooked through, about 2 minutes per side. Transfer the chicken to serving plates.
Toss the arugula and tomatoes in a medium bowl with the remaining 2 tablespoons olive oil, the remaining 1 1/2 tablespoons lemon juice and season with salt and pepper. Divide evenly and mound on top of each chicken cutlet. Top with cheese and serve.
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