Prepare a medium-hot fire in a charcoal grill with a cover, or preheat a gas grill to medium-high.
To make the spread, combine all the ingredients in a small bowl and mix well. Cover and refrigerate until assembling the burgers.
To make the slaw, whisk the mayonnaise, honey, lemon juice, and salt in a small bowl. Combine the cabbage, cucumber, red onion, green onions, cilantro, and chile in a large bowl. Toss with the dressing to coat evenly. Cover and refrigerate until assembling the burgers.
To make the patties, combine all the ingredients in a large bowl. Handling the meat as little as possible to avoid compacting it, mix well. Form the mixture into 6 equal patties to fit the buns, cover, and refrigerate until ready to grill.
To make the potato pancakes, spread the potatoes on a cheesecloth or kitchen towel. Roll up the towel and twist, squeezing out as much liquid as possible. Transfer the potatoes to a bowl. Add the egg, flour, salt, and pepper and stir until combined well.
Pour 1/4 cup of the oil into a 12-inch fireproof skillet and place on the grill. When the oil is hot but not smoking, using half of the potato mixture, place 3 large spoonfuls of the mixture into the skillet, pressing down with a spoon to form three 1/4-inch thick pancakes. Cook, turning once, until brown and crispy, 3 to 4 minutes on each side. Transfer the pancakes to paper towels to drain. Add more oil to the skillet as needed, and repeat with the remaining mixture to make 3 more pancakes.
Brush the grill rack with vegetable oil. Place the patties on the rack, cover, and cook, turning once, until done to preference, 4 to 6 minutes on each side for medium. During the last 2 minutes of cooking, place the buns, cut sides down, on the outer edges of the rack to toast lightly.
To assemble the burgers, spread the dill-feta mixture over the cut sides of the bun tops. Place a patty on each bun bottom. Place a potato pancake on top of each patty and top with equal portions of the slaw. Add the bun tops and serve.
Makes 6 burgers
Suggested Wine Pairing: Chenin Blanc
Contestant Comments: To prevent discoloration of the potatoes, put them in a large bowl of cold water as they are grated. When ready to make the potato pancakes, drain the potatoes well in a colander
Jana Atwood, Boise, Idaho