For the Garlic-Dijon Mayonnaise:
2 tablespoons mayonnaise
1 tablespoon Maille Dijon mustard
1 garlic clove, finely minced
Kosher salt, to taste
For the Burger:1 yellow onion, sliced into ¼ inch rings1 large eggplant, sliced ¼ inch thick
⅓ cup extra-virgin olive oil, divided
Kosher salt and freshly ground black pepper, to taste
1½ pounds ground beef chuck
4 hamburger buns (such as Martin's), toasted
1 medium avocado—pitted, peeled and smashed
1 large beefsteak tomato, sliced ¼-inch thick
¼ cup Maille cornichons with cayenne chili peppers, halved lengthwise
1 cup packed arugula
1. Make the garlic-Dijon mayonnaise: In a small bowl, stir all the ingredients together and season with salt; set aside.
2. Light a grill. Toss the onion and eggplant slices in the olive oil, then season with salt and pepper and place on the grill. Cook, flipping once until charred and tender, 2 to 3 minutes per side. Transfer to a plate and set aside.
3. Make the burger: Transfer the meat to a plastic cutting board and divide into 4 equal portions, about 6 ounces each.
4. Season the burger patties liberally with salt and pepper, and place on the grill. Cook, flipping once, until lightly charred on the outside and medium rare on the inside, 3 to 4 minutes per side. Transfer the patties to a clean cutting board and let them rest for a few minutes.
5. To assemble the burgers, generously spread the garlic mayonnaise on both sides of each burger bun. Place a burger on each bottom bun, then top with a quarter of the mashed avocado, grilled onions, grilled eggplant, sliced tomato, cornichons, arugula and the top bun. Repeat with the remaining burgers and serve.