Slice the chicken breasts in half lengthwise to make cutlets.
Season with salt and pepper, then dredge lightly in flour.
Heat the olive oil and butter in a large skillet over medium-high heat.
Sear the chicken until golden and cooked through, about 4 to 5 minutes per side, then transfer to a plate.
Add the garlic, sun-dried tomatoes, chipotle, and oregano to the same skillet and cook for 1 minute.
Pour in the broth and scrape up the browned bits.
Stir in the cream and simmer for 2 to 3 minutes, until slightly thickened.
Stir in the Parmesan and lime juice until the sauce turns smooth and glossy.
Return the chicken to the skillet and spoon the sauce over the top.
Simmer for 1 to 2 minutes, then finish with cilantro.