Chicken Parmesan Panini

INGREDIENTS

• 2 boneless, skinless chicken breasts
• Kosher salt and freshly ground pepper, to taste
• 1 cup vegetable oil, plus more for brushing
• 4 sandwich rolls, split
• 3/4 cup all-purpose flour
• 2 eggs, beaten
• 1 cup dry bread crumbs
• 3/4 cup finely grated Parmigiano-Reggiano cheese
• 1 1/3 cups shredded mozzarella cheese
• 1/4 cup thinly sliced fresh basil
• 1 cup tomato sauce