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1
In a bowl, mix together the meat, 1/4 cup pesto, and 1 1/2 teaspoons pepper. Handling lightly to keep the texture light and juicy, divide the meat into 4 evenly sized, thick patties. The burgers can be shaped and refrigerated, covered, for several hours or overnight.
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2
When ready to cook, heat the olive oil in a large skillet or grill pan over medium-high heat until very hot or build a medium-hot fire in a barbecue. Generously season the meat on both sides with salt and pepper.
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3
Cook the burgers in the skillet, turning once or twice, for 7 to 10 minutes for medium-rare. Do not press down on the patties. With a large spoon, baste the burgers several times with the fat in the pan. (You can also preheat the oven to 450u00b0F and cook the burgers on top of the stove until they are brown on both sides, and then finish them in the oven.) To grill the burgers, oil the grate, arrange the patties on it, and cover. Cook as above.
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4
For the last minute or two of cooking, drape a slice of cheese over each burger to melt. Then remove them to a warm platter, keep warm, and let rest for several minutes before serving.
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5
While the burgers cook, toast the buns in a toaster oven or under the broiler, about 5 inches from the heat, until lightly toasted. Or toast on the outer perimeter of the grill rack.
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6
To build the burgers, spread the bun bottoms with about a tablespoon of the remaining pesto. Top with the tomato slices and then the arugula. Add the burgers and then a grilled onion on top of each. Sprinkle with fleur de sel, if using. Cover with the bun tops. Serve immediately with any remaining pesto on the side.
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7
Trim the larger stems off the cilantro and discard them. Put the nuts and garlic in a food processor and process until they are finely chopped. Add the cilantro, arugula, lime juice, and lime zest, and process until you have a coarse puree. With the machine running, add the olive oil in a thin stream and process until smooth. Scrape down the sides as necessary. Pulse in the cheese and season to taste with salt and pepper. Transfer the pesto to a container, cover, and refrigerate until needed, or for up to 2 days.
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8
Build a medium-hot fire in a barbecue. Clean and oil the grate.
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9
In a small bowl, whisk together the 2 tablespoons of olive oil, mustard, honey, and vinegar. Set aside.
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10
Peel the onions, leaving the ends intact, then cut them crosswise into 1/2-inch-thick slices. Reserve the ends and small slices for another use. You should have about 4 good slices per onion. Holding them flat on the counter, thread one or two skewers through each slice, placing the skewers parallel and about 1 1/2inches apart. Make sure one skewer goes through the centermost rings. The skewers will hold the slices together while they cook. Trim the skewers, if necessary, to fit on the grill.
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11
When ready to cook, brush the onions on both sides with olive oil and season with salt and pepper. Arrange them on the grate and grill, turning after they have browned on the first side. Cook until they are about half done then brush them with the mustard mixture. Be careful, as the mixture may cause flare-ups. If so, move the onions to a cooler part of the grate. Turn and brush the onions with the mustard mixture several times, until tender throughout and the outsides have caramelized, about 15 minutes. Transfer the onions to a plate and keep warm. Remove the skewers before serving.
