Heat a large sauté pan over medium heat. Add olive oil, garlic, and chile flakes. Stir, cooking until the garlic is lightly golden and fragrant, about 2-3 minutes.
Add the crushed tomatoes and season with salt, black pepper, and basil. Bring the sauce to a simmer and cook for 10 minutes, stirring occasionally. Set aside.
On a clean work surface, butterfly the chicken breasts.
Cover with plastic wrap, and use a rolling pin or meat mallet to pound out the chicken to ¼-inch (6-mm) thick.
Season each side with salt and black pepper.
With the cut side of the chicken facing up, arrange a flat layer of 4 half slices of ham, followed by 4 half slices of mozzarella.
Roll toward you, starting the with the thickest part of the chicken. Wrap tightly in plastic wrap and chill in the fridge for 30 minutes.
Place the panko in a wide, shallow bowl, and add the Parmesan cheese and oregano. Stir to incorporate. Prepare two more wide bowls with the flour and the beaten egg.
Unwrap the chicken and dredge in the flour, eggs, then bread crumbs.
Heat the oil in a large pot until it reaches 325°F (170°C). Add the chicken, two rolls at a time, and cook about 5 minutes per side or until the outside is an even golden brown. If a good color is achieved and the chicken’s center is still not 165°F (74°C), you can finish cooking the chicken in an oven set to 325°F (170°C) until that temperature is reached.
Place the fried chicken in an ovenproof dish. Spoon the tomato sauce over the top, saving some for serving.
Arrange fresh mozzarella slices on top.
Broil on the center rack for 8-10 minutes, until the cheese is melted and has small brown bubbles.
Garnish with fresh basil and serve with the reserved tomato sauce alongside.