1 pineapple, peeled, cored, and cut into ½-inch-thick rings (you will need 4 rings for this recipe)
4 tablespoons prepared mayonnaise
1 tablespoon prepared harissa (we like Dea Harissa Hot Sauce)
2 cups seasoned rice wine vinegar
2 tablespoons honey
2 pounds ground beef chuck, preferably grass-fed, not too lean
1 teaspoon whole coriander seed
1 teaspoon whole black peppercorns
4 tablespoons (1/2 stick) unsalted butter, divided
2 tablespoons extra-virgin olive oil
1/2 teaspoon dry mustard
4 slices prepared pickled beets
2 heaping teaspoons peeled and thinly sliced fresh ginger
4 large eggs
zest and juice of 1 lime
coarse salt and freshly ground black pepper
4 ciabatta buns
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.
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.