Preheat a nonstick grill pan over medium-high heat.
Roughly chop 6 of the bacon slices, and add to the grill pan. Cook, stirring occasionally, until the bacon just barely begins to turn crispy, about for 3 to 4 minutes. Add the cooked bacon to a food processor and process for 4 to 5 seconds. Set aside for later use, (in the patties).
Honey Molasses-Glazed Bacon:
In a small mixing bowl combine the honey, molasses, vinegar, and cayenne and mix until well combined. Brush the remaining 12 bacon slices on both sides with the honey mixture. Heat a large fireproof nonstick skillet on the grill. Add 1/2 the bacon and cook over medium-high heat until crispy, about 5 minutes, flipping once. Drain on paper towels. Repeat with remaining bacon.
To make Grilled Lettuce: Soak the radicchio leaves, for about 10 minutes, in an ice bath to lessen the amount of bitterness. Remove the leaves from the ice bath and pat dry with paper towels. Brush the leaves with 1 tablespoon oil. Put on the grill and cook briefly on each side. Transfer to a cutting board and cut into 1-inch wide strips. In a large mixing bowl, whisk together the remaining 1 tablespoon of oil, the sherry vinegar, and Dijon mustard. Add the radicchio and toss to coat.
Smoky Tomato Mayo: Put the tomato on the grill and cook for 6 to 8 minutes, turning occasionally, until most of the skin has blackened. Transfer to a small bowl and cover with plastic wrap. After 10 minutes, squeeze the tomato into a strainer to remove the seeds and most of the skin (you can leave a little bit of the burnt skin). Discard the seeds and skin. In the bowl of a food processor, combine the tomato, smoked paprika, garlic, and mayonnaise and puree. Season, to taste, with salt and pepper.
Patties: Combine the beef, reserved bacon (that has been chopped in the food processor), tarragon, salt, and pepper in a large bowl. Mix well, handling the meat as little as possible to avoid compacting. Divide the mixture into 6 equal portions and form into patties to fit the size of the buns.
Brush the grill pan with vegetable oil. Arrange the patties in the pan and cook, turning once, just until done, about 4 minutes on each side for medium-rare. During the last few minutes of cooking, top with equal amounts of cheese and put the buns, cut side down, on the outer edges of the grill to toast lightly.
To assemble the burgers, spread a generous amount of the Smoky Tomato Mayo on the cut side of the buns. Top the bun bottoms with 2 slices of Honey Molasses-Glazed Bacon, a cheese-topped patty, and equal amounts of Grilled Lettuce. Cover with the bun tops and serve.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.