How to Make It
Stir together mayonnaise,shallot,cornichons,chives,green peppercorns,cognac,and lemon juice in a medium bowl;season to taste with salt.Chill.
Cut chuck and rib eye into 3- x 3/4-inch strips.Follow instructions for grinding beef using thegrinding technique here through step 5.
Shape ground beef into 6 tightly packed (4-inch-wide) patties.Heat 2 teaspoons oil in a large skillet over medium-high;add 3 patties,and season tops evenly with 1/2 teaspoon salt.Cook until well browned on bottoms,about 4 minutes.Flip burgers,and season evenly with 1/2 teaspoon salt and 1/2 teaspoon black pepper;cook to desired degree of doneness,about 4 minutes for medium.Transfer patties to a plate,and tent with aluminum foil to keep warm.Wipe any excess salt from skillet.Repeat with remaining 2 teaspoons oil,remaining 3 patties,remaining 1 teaspoon salt,and remaining 1/2 teaspoon pepper.
Serve patties on brioche buns with sauce,red onion,and crispy fried onions.