Place the chicken breast cutlets between two sheets of plastic wrap. Using a meat mallet, pound them to an even 1/4-inch thickness to ensure even cooking.
Set up a breading station with three shallow bowls: place the flour in the first; whisk the eggs and mayonnaise together in the second; and combine the breadcrumbs, chopped parsley, chopped basil, and salt in the third.
Dredge each chicken cutlet in the flour, shaking off any excess. Dip it into the egg mixture to coat completely, and finally press it firmly into the breadcrumb mixture until evenly coated on both sides.
Heat the olive oil in a large skillet over medium-high heat until shimmering. Working in batches, carefully add the breaded chicken cutlets and pan-fry for 3 to 4 minutes per side, until deeply golden brown and cooked through (165°F internal temperature).
Transfer the cooked cutlets to a wire rack set over a baking sheet to drain excess oil. Sprinkle immediately with a pinch of salt.
In a medium bowl, toss the baby arugula and halved cherry tomatoes. Squeeze the juice from two lemon wedges over the salad, add a drizzle of olive oil, and season lightly with salt.
Serve the warm, crispy chicken cutlets immediately, topped generously with the fresh arugula and cherry tomato salad. Garnish with the remaining lemon wedges.