For the poblano and pepper jack-stuffed chicken breasts: Roast the poblano peppers over an open flame until completely charred, transfer to a plastic bag and seal for 10 minutes. Peel the charred skin, remove all the seeds and cut each pepper in half.
Meanwhile, put chicken breasts on a cutting board and pound with a meat mallet to 1/4-inch thickness. Season with salt and pepper.
Heat a large skillet over medium high heat. Add the oil, heat, then add the chicken and cook until the first side is golden-brown, 1 to 2 minutes. Flip and cook until the second side is golden-brown, another 1 to 2 minutes. Transfer the skillet to the oven and roast until just cooked through, about 8 minutes.
Meanwhile, make the ancho chile cream sauce: Bring the cream to a simmer in a small saucepan and cook until reduced by 1/3. Add the Cajun spice and ancho chile powder and simmer for another minute or so. Keep warm.
When the chicken is done, cut each piece into 2 equal halves. Lay one piece in the centers of 2 dinner plates and top each with 2 poblano halves, 1 piece of pepper jack, and another piece of chicken. Pour half of the Ancho Chile Cream Sauce over the tops and serve immediately.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.