2 egg yolks
Juice of 2 small lemons (about 6 tbsp.)
2 cloves garlic, crushed
2 tsp. Dijon mustard
4 anchovy fillets About 3/4 to 1 cup EVOO
8 green Cerignola olives or other fatty olives, pitted
3 tbsp. drained Italian capers
Salt and pepper
2 lb. coarsely ground best-quality beef
2 tbsp. Worcestershire sauce
Kosher salt and black pepper
Olive oil, for drizzling
2 tbsp. butter
A fat sprig of rosemary
1 large clove garlic, crushed
4 slices (1/4 to 1/2 inch thick) fresh mozzarella or 4 thick slices mild provolone (from the deli counter)
Crusty soft rolls (such as plain or sesame kaiser rolls or round Italian sandwich rolls), split and lightly toasted
Sliced red or white onion, sliced ripe tomatoes, and shredded escarole or romaine, for topping
Giardiniera (hot pickled vegetables in brine) and fancy potato chips, for serving
In a food processor, add the egg yolks, lemon juice, garlic, Dijon, and anchovies. With the machine running, stream in the EVOO; run the machine until the aioli is emulsified. Add the olives and capers and pulse into the aioli. Season with salt and pepper.
Heat a large cast-iron griddle or skillet over medium-high to high. In a medium bowl, mix the beef with the Worcestershire; season with kosher salt and black pepper. Form into 4 large patties (thinner in the centers for even cooking). Drizzle the pan with olive oil. Add the patties and cook, about 5 to 6 minutes for rare or 7 to 8 minutes for medium-rare. Add the butter, rosemary, and garlic to the pan. Using a large spoon, baste the patties with the garlic-rosemary butter; top with the cheese. Tent the pan loosely with foil to melt the cheese, about 1 minute.
Build the burgers by stacking the roll bottoms, onion, tomatoes, burgers, and escarole. Slather the roll tops with the garlicky aioli and place on top. Serve the giardiniera and fancy potato chips on the side.