Wash and dry all produce. Preheat oven to 450 degrees. Cut potatoes into ½-inch cubes.
Toss potatoes on a baking sheet with a large drizzle of olive oil and a pinch of salt and pepper. Roast in oven until browned, 20-25 minutes, tossing halfway through.
In a small bowl, combine panko, mozzarella, a large drizzle of olive oil, and a pinch of salt and pepper.
Place chicken on another, lightly oiled baking sheet. Brush 1 TBSP pesto onto top of each piece (you will have a little pesto left over). Press crust mixture into pesto to adhere. Roast in oven until chicken is no longer pink in center, about 20 minutes.
Halve lemon. In a large bowl, toss together mixed greens, a squeeze of lemon, and 4 tsp olive oil. Season with salt and pepper.
Divide potatoes and chicken between plates. Serve with salad on the side.