Before making burgers, soak ¼ cup roughly chopped dried figs in a small bowl with 3 tablespoons of Spanish sherry (amontillado) for several hours or overnight. Prepare and chill the sherry vinaigrette.
Drain the figs (reserving the liquid for the vinaigrette and setting the soaked figs aside). Mix the first six ingredients together in a small bowl. Whisk in the olive oil at the end to emulsify, then chill.
Place the lamb and the rest of the ingredients in a large bowl and mix together. (Handle the lamb as little as possible to avoid compacting it.)
Flatten into patties and make a slight depression in the center of each, which ensures even cooking.
Wrap the patties in plastic wrap and chill for at least an hour before cooking.
Allow the burgers to cool briefly before placing atop the salad and dressing.
Once you’ve made the patties, use your thumbs to make a deep well in the center of each patty and fill each with a quarter of the soaked figs and 2 tablespoons of the manchego. Pull some ground lamb up to cover.
Flatten again into patties.
To cook, sear the patties in a cast-iron skillet or on the grill for about 3 to 4 minutes per side (for pink in the center), until slightly charred, flipping once.
Serve over field greens, baby arugula, Johnny-jump-ups or other viola flowers, red grapes, thin slices of oranges and red onions, green onions, black olives, toasted pine nuts, hazelnuts or Marcona almonds and garlicky croutons, and pass the sherry vinaigrette at the table.