In a large saute pan over medium heat, add enough oil to have about 1/2 inch depth. Let it heat about 3 minutes. Gently "pass each tortilla through the oil," one by one, for about 15 seconds on each side, they will soften and become resilient. You should be able to fold them without breaking them. Transfer them to a paper towel covered plate.
Preheat the oven to 375°F.
Place about 2 to 3 tablespoons chicken inside of each tortilla and roll them up. Place them, seam side down on a baking dish. Cover, generously, with the green sauce. Place them in the oven for 10 to 15 minutes. Remove them from the oven, sprinkle with the crumbled cheese, the cream, and the chopped onion. They are very satisfying with a side of rice and/or beans, as well as with a light green salad.
Eat the enchiladas while they are hot!