To make the patties: Combine the beef, oregano, salt, garlic powder, and pepper to taste in a medium bowl and mix well. Shape into patties a little more than 1/2-inch thick, place on a plate, and refrigerate for at least 1 hour.
To make the sauce: Stir together the sour cream, chipotles, adobo sauce, onions, cilantro, salt, and pepper to taste in a small bowl. Set aside.
To make the burgers: Oil a grill rack and preheat the grill on high for 5 minutes. Spread the bun faces lightly with the butter. Grill the burgers over direct heat on medium-high (on a charcoal grill, set the burgers just outside the center of the grill rack), with the grill covered, for 4 minutes. Flip the burgers, top each with a slice of Cheddar, and grill, covered, 4 minutes more. Remove the burgers to a plate.
Grill the buns, buttered-side down, over indirect heat, until golden, about 2 minutes. Set a burger on each bun bottom and top with avocado, tomato, lettuce, red onion and a dab of chipotle sauce. Top with the remaining bun halves and serve.
Adapted from "One Dish at a Time: Delicious Recipes and Stories from My Italian-American Childhood and Beyond" by Valerie Bertinelli © Rodale 2012. Provided courtesy of Valerie Bertinelli. All rights reserved.