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Recipe courtesy of "The New Brooklyn Cookbook" by Melissa Vaughan and Brendan Vaughan, copyright 2010. Reprinted by permission of William Morrow Cookbooks/HarperCollins Publishers.
| 1 pineapple, peeled, cored, and cut into ½-inch-thick rings (you will need 4 rings for this recipe) | 4 tablespoons prepared mayonnaise | |
| 2 cups seasoned rice wine vinegar | Zest and juice of 1 lime | |
| 2 tablespoons honey | 2 pounds ground beef chuck, preferably grass-fed, not too lea | |
| 1 teaspoon whole coriander seed | Coarse salt and freshly ground black pepper | |
| 1 teaspoon whole black peppercorns | 4 tablespoons (1/2 stick) unsalted butter, divided | |
| 2 tablespoons extra-virgin olive oil | 4 ciabatta buns | |
| 1/2 teaspoon dry mustard | 4 slices prepared pickled beets | |
| 2 heaping teaspoons peeled and thinly sliced fresh ginger | 4 large eggs | |
| 1 tablespoon prepared harissa (we like Dea Harissa Hot Sauce) |
Place 4 pineapple rings in a large heat-proof glass or stainless-steel bowl. In a medium nonreactive saucepan, combine the vinegar, honey, coriander seed, peppercorns, olive oil, mustard, and ginger. Bring to a boil and cook for 5 minutes. Pour the mixture over the pineapple, cover with plastic wrap, and refrigerate overnight.
Combine the harissa, mayonnaise, and lime zest and juice in a small bowl and set aside.
Prepare the grill for cooking or heat a ridged grill pan over medium-high heat until hot. Remove the pineapple from the marinade and grill for 2 minutes per side.
Season the beef with salt and pepper and form into 4 burgers. Grill the burgers, covered only if using a gas grill, turning once, about 5 minutes total for rare or 6 minutes for medium-rare.
Melt 2 tablespoons of the butter. Lightly brush the cut side of the buns with butter and grill for 1 or 2 minutes. Spread the harissa mayonnaise on the grilled buns.
In a nonstick pan, melt the remaining 2 tablespoons butter over medium-low heat. Break each egg into a small bowl and add it to the pan. Gently fry the eggs until the whites are set (sunny-side up), taking care not to break the yolk.
Place a burger on the bun and top each burger with a pickled beet slice, grilled pineapple slice, and sunny-side-up egg.