How to Make It
In a large resealable plastic bag, mix the feta brine and hot sauce. Add the chicken cutlets, seal the bag and turn to coat. Refrigerate for 30 minutes.
Meanwhile, in a food processor, pulse the feta cheese and lemon juice. Slowly blend in the 1/3 cup of oil until smooth. Season with salt and pepper.
Preheat a grill pan. Remove the chicken from the brine and pat dry; discard the brine. Brush with oil and season with salt and pepper. Grill the cutlets over moderately high heat, turning once, until cooked through, about 5 minutes total.
Spread the rolls with some of the feta. Top with the chicken, arugula, cucumber, onion and peppers and serve.