For the chile stuffing: Preheat a grill to high heat (you can also use a broiler if you don't have a grill). Place the whole chiles on the grill and cook until well charred and blistered, turning every 2 to 3 minutes. Transfer to a heatproof bowl and cover with plastic wrap so they "sweat," making them easier to peel. Let the chiles stand for 5 minutes before uncovering and using towels to rub off the skins. Discard the skins, remove the cores and seeds and finely chop the chiles. Transfer to a large mixing bowl and season with salt and pepper. Add the cheeses and stir together to form a stuffing. Set aside until ready to use.
For the turkey cordon bleu: Make a horizontal cut down the length of the thin side of each turkey breast using a sharp thin knife. Open the breasts up like a book so the cut-sides are exposed facing up and the skin-side is down, with the "spine" of the chicken horizontal on your work surface. Sprinkle the turkey with salt and pepper.
Lay 5 slices of the deli ham on each breast and trim the edges so the ham fits inside the breast and there is a small border around the turkey. Leaving this gap will ensure that when the turkey is rolled up it forms a nice seal and the stuffing doesn't ooze out everywhere. Divide the poblano-cheese stuffing in thirds and spread on each of the breasts evenly, leaving a small border around the edge. Starting from one side, tightly roll up the turkey away from you, stuffing in any of the filling as it tries to escape at the edges (it is important you roll it up this way, so when you make the slices in the finished roulade they are across the grain). Secure the roll with pieces of butchers twine every 2 inches to form a tight, even log. Repeat with the remaining breasts. Sprinkle the outsides with salt and pepper.
Preheat the oven to 375 degrees F. Heat oil in a turkey roaster set across two burners on medium-high heat. Add the roulades and brown evenly, 3 to 4 minutes per side. When browned all over, transfer the whole pan of the roulades to the oven and finish cooking. Roast until the internal temperature reaches 160 degrees F, 30 to 35 minutes.
Transfer to a platter and allow the meat to rest to allow for carry-over cooking and the internal temperature to reach 170 degrees F, 10 to 12 minutes. To serve, remove the twine and cut into 1/2-inch-thick slices. Drizzle the pan juices over the top.