For the pickles: Place the zucchini slices and oregano in a large jar or heat-safe container. Heat the apple cider vinegar, sugar, peppercorns, salt, fennel seed, red pepper flakes and bay leaf in a medium saucepan, stirring until the sugar and salt have dissolved, about 2 minutes. Pour the pickling liquid and spices into the jar. Let cool completely, uncovered. Place in the refrigerator for at least 24 hours and store for up to 6 weeks.
For the frico: Place an oven rack in the center of the oven and preheat the oven to 375 degrees F. Line a baking sheet with parchment paper or a silicone mat. Toss the Parmesan, flour and pepper together in a large bowl, making sure the flour is evenly distributed throughout the cheese. Arrange mounds of 2 tablespoons of cheese 4 inches apart on the baking sheet and flatten each mound slightly with a spatula to form a 3-inch round. Bake the frico in the oven until golden brown, about 10 minutes, rotating the sheet halfway through baking. Cool the frico on the baking sheet for 2 minutes, and then gently transfer to a wire rack to cool completely.
For the mayo: In a small bowl, stir together the mayo, garlic, lemon juice, parsley, oregano, salt and pepper.
For the patties: In a large bowl, combine the beef, lamb, salt and pepper. Form the mixture into six 4-inch-diameter patties, each about 1/2-inch thick. Drizzle the patties with olive oil. Place a grill pan over medium-high heat or preheat a gas or charcoal grill. Grill the patties until they are grill marked and cooked through, about 4 to 5 minutes per side. Allow the patties to rest for 5 minutes.
For the burgers: Drizzle the cut side of the ciabatta rolls with olive oil and grill lightly until toasted, about 1 to 2 minutes. Spread the garlic mayo over the bottom halves of the grilled bread. Place the burger patties on the bread and top each patty with 2 tomato slices, 4 pickle slices and 1 frico round.
To roast the garlic, preheat the oven to 400 degrees F. Cut a garlic bulb in half crosswise and place the halves on a sheet of foil. Drizzle each cut side with 1 teaspoon of olive oil and sprinkle with 1 teaspoon of kosher salt. Fold the foil up around the garlic halves and the seal the foil into an airtight package. Roast until golden and soft, about 1 hour.