In a medium stockpot, combine chicken, broth, wine, pepper, oregano, 2 tsp salt, juice from 1 1/2 limes, and water to cover chicken fully. Bring to a boil, reduce heat, and simmer until chicken is cooked through.
Cool chicken for about 15 minutes and remove from the broth. Retain broth for future use, if desired. Cut or shred chicken into small pieces.
In medium bowl, mix yogurt, half and half, 1/2 tsp kosher salt, the juice of one lime, and 1/3 cup white wine.
Preheat oven to 400. Lightly grease a 9×13 baking pan.
If using corn tortillas, heat a small amount of oil over medium heat to soften each tortilla. It should only take a few seconds on each side. Pat off excess oil with a paper towel.
Fill each tortilla with about 1/3 cup chicken and some sauce. Roll tortilla up and place into prepared pan, with open side down. Top with the sauce, onions and cheddar cheese. Cover with foil and bake for 20-25 minutes, making sure the cheese melts and the enchiladas are heated throughout.