To make the Chipotle Mayo, in a small bowl, stir together the mayonnaise, chipotle, lime juice, and salt. Refrigerate.
To make the burgers, in a medium skillet, heat 1 Tbs. oil over medium heat. Add onion, 1/2 tsp. salt, and oregano. Cook, stirring occasionally, until the onion is tender and starting to brown, 5 to 6 minutes. Remove from heat.
In a large bowl combine the cooked onion, turkey, breadcrumbs, egg, adobo sauce, remaining 1/4 tsp. salt, and black pepper to taste. Mix until thoroughly combined. Form into eight 1/2-inch-thick patties.
Heat a grill, grill pan, or large, heavy skillet over medium heat. Brush lightly with oil. Grill or cook patties for 8 to 10 minutes or until no longer pink (165°F), turning once halfway through grilling and adding the cheese (if using) during the last 3 minutes of cooking.
Spread cut side of bottom buns with refried beans. Spread cut side of top buns with Chipotle Mayo. Serve burgers in buns with avocado slices.