Make the patties: heat the oil in a large sauté pan over medium-high heat. Add the mushrooms and cook until they have dehydrated and are brown and crispy, 8 to 12 minutes. Season with salt and pepper to taste. Transfer the mushrooms to a food processor and pulse until finely chopped.

In the same sauté pan, cook the fennel over medium heat until caramelized, about 10 minutes. Add the garlic and rosemary and cook for an additional 1 minute. Remove from the heat and let cool for 10 minutes.

In a large bowl, use your hands to mix the cooled mushrooms and fennel mixture with the ground wild boar meat until well combined. Shape into four 5 1/2-ounce patties. Season the patties with salt and pepper to taste before grilling.

Make the aïoli: add all ingredients to a food processor and purée until blended, making sure to scrape down the sides of the bowl to incorporate all of the ingredients. (Note: the aïoli will last for 2 weeks in the refrigerator.)

Sauté the broccoli rabe: heat the oil in a large skillet over medium-high heat. Add the broccoli rabe and cook until the stalks are soft and the leaves and beginning to crisp, 5 to 7 minutes. Season with salt and pepper to taste.

Roast the tomatoes: heat the oven to 350°F. Toss the sliced tomatoes with the olive oil, garlic, and salt and pepper taste. Transfer to a baking sheet and roast until caramelized, about 25 minutes.

Cook the burgers: heat a well-oiled cast-iron skillet over medium-high heat. Once the pan is hot, cook the patties until they’re seared on one side, about 3 minutes. Flip and repeat until seared on the other side, about 3 minutes. Add the provolone slices on top of each patty in the last minute of cooking.

To serve: spread a thin layer of the aïoli on both sides of the ciabatta bun. Add the burger, broccoli rabe, roasted tomatoes, and top with the other half of the bun.