Preheat oven to 425°. In a nonstick skillet, simmer the chicken, salsa, onion, cumin and oregano until ingredients are heated through and most of the liquid has evaporated.
Place 1/2 cup chicken mixture down the center of each tortilla; top with 2 tablespoons cheese. Fold sides and ends over filling and roll up.
Place seam side down in a 13x9-in. baking dish coated with cooking spray. Bake, uncovered, until lightly browned, about 15 minutes.
Meanwhile, in a small saucepan, combine the broth, bouillon and pepper. Cook until bouillon is dissolved. In a small bowl, combine flour and half-and-half until smooth; gradually stir into broth. Bring to a boil; cook and stir for 2 minutes or until thickened. Stir in chiles; cook until heated through. Serve with chimichangas.