Combine the chiles with the shredded cheese and cream cheese in a medium bowl. Stir to combine. Set aside.
Combine the beef with 1 teaspoon salt and 1/2 teaspoon pepper in a medium bowl. Gently mix with your hands and form into 8 equal balls.
Flatten 2 of the beef balls into patties and place about 1 tablespoon of the adobo cheese filling between the 2 patties. Pinch around the edges to seal and enclose the filling. Repeat with the remaining beef to form a total of 4 stuffed patties.
Heat the oil in a large skillet over medium-high heat and cook the burgers until well-browned, 3 to 4 minutes per side.
Spread the mayonnaise on the split sides of the buns. Top the bottom buns with the onion, lettuce, tomato and stuffed patties. Close the burgers and serve.