Rub a cast-iron skillet or griddle pan with the oil; heat over medium-high.
In a medium bowl, combine the ground beef, chiles, onion, Worcestershire sauce, garlic and cumin; season with salt and pepper. Form into 4 patties, thinner in the centers for even cooking. Add the patties to the skillet and cook, turning occasionally, until browned, about 8 minutes. During the last minute or so of cooking, top each burger with 1 slice of each cheese, stacking askew to form an eight-pointed star. Tent the pan loosely with foil to melt the cheese. Place the patties on the English muffin bottoms; top with some pickled jalapeño slices.
In a large nonstick skillet or griddle, melt the butter over medium. Crack the eggs into the skillet and fry to desired doneness, 2 to 4 minutes; season. (I recommend sunnyside up or over easy.) Put the eggs on top of the burgers, then add the English muffin tops.