If using chicken breasts, start from the thickest end and slice each chicken breast in half horizontally so you end up with a total of 6 cutlets.

Dry the chicken well with paper towels. Season both sides of the chicken cutlets liberally with salt and pepper.

Scatter the flour on a large plate and dredge the cutlets, shaking off any excess flour. Transfer the cutlets to a sheet pan or large platter in a single layer.

Heat the oil in a large sauté pan over medium-high. When the oil begins to ripple, reduce the heat to medium and add the butter.

As soon as the butter melts, add the cutlets and cook until golden on one side, about 5 minutes. Flip the chicken and cook the other side until golden, 4 to 5 minutes. Do this in batches, if needed, adding more oil, if needed. Transfer the cutlets to the platter or sheet pan.

Reduce the heat to low, add the garlic and cook, stirring often, until fragrant, 1 to 2 minutes.

Add the tomato paste and crushed red-pepper flakes, stirring until the color deepens, about 2 minutes.

Add the oregano.

Increase the heat to medium, add the stock and bring to a simmer, scraping up any bits from the bottom of the pan, until the liquid is reduced by half, about 5 minutes.

Add the cream and warm through, stirring, until it thickens slightly, about 3 minutes. Watch the cream closely, reducing the heat if necessary, to maintain a gentle simmer.

Stir in the Parmesan and the sun-dried tomatoes. Place the chicken back in the pan, flipping to coat with the sauce, and warm through, about 4 minutes.

Remove from the heat, scatter basil on top, and serve on warmed plates.