Arrange three medium-size bowls on the counter and fill one with the flour, one with the eggs and one with a mixture of the breadcrumbs, cheese, garlic, lemon zest and parsley.
Season the chicken pieces with salt and freshly ground black pepper, and coat each piece first in the flour, then the egg and finally in the breadcrumb-cheese mixture.
Place a large pan over medium-high heat with 3 tablespoons EVOO, about 3 turns of the pan. Cook the chicken pieces in 2 batches, turning once, until golden brown and cooked through, 5-6 minutes.
While the pieces are cooking, place a medium-size pot over medium-high heat with the crushed tomatoes and bring up to a bubble. Remove the pot from the heat and stir in the pesto.