Green-Chile Burgers with Fried Eggs
- 2 ¼ pounds ground chuck, preferably organic
- Salt and freshly ground pepper
- ½ pound mild American blue cheese, such as Maytag Blue Cheese, cut into 4 thin slices
- 4 large eggs
- 4 brioche buns, split
- 4 tablespoons unsalted butter, melted
- Vegetable oil
1 Cup Green-Chile Relish, warmed up
Green Chili Relish
- 1 pound long green New Mexico or Anaheim chilies
- 3 garlic cloves, minced
Roast the chilies over a gas flame or under a preheated broiler, turning often, until charred all over. Transfer to a large plate and let cool. Discard the charred skin, seeds and stems and cut the chilies into ½ inch dice. Transfer the chilies to a bowl and stir in the garlic. Season with salt and pepper. The green chili can be refrigerated for up to 3 days.
Light a grill. Gently form the beef into 4 thick patties and season with salt and pepper. Grill over moderately high heat until lightly charred on the outside and medium-rare within, about 5 minutes per side. Just before the burgers are done, top each one with a slice of cheese and lit it melt. Meanwhile, heat a large cast-iron skillet and brush it lightly with oil. Crack the eggs into the skillet and cook sunny-side up over moderate heat, about 4 minutes. Spread the cut sides of the buns with the melted butter and toast on the grill. Transfer the burgers to the buns. Top with the Green-Chile Relish and fried eggs and serve.