In the bowl of a food processor, combine the parsley, basil, thyme, shallot, garlic, lemon juice, and Dijon mustard and puree until smooth. Add the butter and pulse until well combined. Transfer to a small bowl and reserve.
Heat a large nonstick skillet over medium-high heat. Sprinkle 1/2 of the cheese into 2 to circles (approximately 4 1/2-inch in diameter) in the skillet. Cook for 2 minutes. Then carefully flip with a spatula and cook for another 1 minute. Drain on paper towels. Repeat with remaining 1/2 of the cheese.
Meanwhile, to make the speck, heat the oil in a large skillet over medium-high heat. Add the speck and cook until crispy, stirring occasionally, about 5 minutes. Remove from the skillet and drain on paper towels.
To make the patties, put capicola and rosemary in the bowl of a food processor and pulse until finely chopped. In a large mixing bowl, combine the capicola mixture, chuck, salt, and pepper; mix well. Separate the mixture into 4 equal portions and form the portions into patties to fit the size of the buns.
Heat large skillet or grill pan over high heat. Add the patties to the skillet and cook for 3 1/2 minutes. Flip the burgers and cook for 3 to 4 minutes or to desired doneness. During the last few minutes of cooking, top the burgers with equal amounts of fontina cheese and tent with aluminum foil to melt cheese. Also, during last few minutes of cooking, toast the buns.
To assemble the burgers, spread a generous amount of Italian Herb Butter on the cut sides of the buns. On each bun bottom, arrange equal amounts of pine nuts, Crispy Speck, arugula, a patty topped with cheese, and a Frico. 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.