Preheat oven to 350°. Spray a 13 x 9-inch pan with cooking spray; set aside.

In a skillet large enough to hold a corn tortilla, add Salsa Verde, pepper, chicken broth and lime juice. Bring to a boil and reduce heat to low. Puree the mixture until smooth and add the sugar, one teaspoon at a time, until it is slightly sweet.

In a skillet, heat olive oil over medium heat. Add onions and cilantro and cook until onions are transluscent. Add garlic, salt and pepper and cook for 1 minute more. Raise heat to medium high and add shrimp. Stir and toss the shrimp until they just turn pink. Put mixture in bowl and set aside, or refrigerate.

In skillets large enough to fit the flat corn tortillasheat the olive oil and enchilada sauce over medium heat. When oil is shimmering, or when a toothpick put in the oil causes the oil to bubble, fry the tortillas, one at a time, until crisp at the edges. Put one tortilla at a time into the hot enchilada sauce, just until the tortillas is softened. Put the tortilla on a plate and place shrimp down the middle of the tortilla, along with a line of the grated cheese. Roll the tortilla into a tube and place, seam side down, in a 9 x 13-inch pan that has been sprayed with cooking spray. Repeat until you have filled all the enchiladas, placing one next to the other. Bake in a preheated 350° oven for 15 minutes.

Remove from oven and put 2 or 3 enchiladas per plate. Spoon sauce over the enchiladas until well-covered and top with grated cheese. Put under broiler for 1 to 2 minutes, until cheese is melted, and serve.