Make the aioli: Blend the mayonnaise, sun-dried tomatoes, garlic, fresh herbs and 1/4 teaspoon each salt and pepper in a mini food processor or blender until smooth. Transfer to a bowl and refrigerate until ready to use.
Make the roasted tomatoes: Preheat the oven to 425 degrees F and line a baking sheet with parchment paper. Pat the tomatoes dry with paper towels and arrange on the prepared baking sheet; drizzle with the olive oil and sprinkle with the dried basil, oregano and 1/2 teaspoon each salt and pepper. Roast until the tomatoes start caramelizing, about 30 minutes.
Meanwhile, make the caramelized onions: Melt the butter in a large skillet over medium heat. Add the onions and sugar and toss to coat. Cover and cook, stirring occasionally, until golden, about 20 minutes. Increase the heat to medium high and cook, stirring, until browned and caramelized, 15 to 20 more minutes; season with salt and pepper. Remove from the heat and set aside.
Make the burgers: Preheat a grill to medium high and brush the grates with vegetable oil. Put the beef and sausage in a large bowl and combine with your hands. Form four 3/4-inch-thick patties; season with salt and pepper. Grill the burgers until the edges begin browning, 3 to 5 minutes, then flip and top each patty with a slice of cheese. Cover and cook until the cheese is melted and the burgers are done, 3 to 4 more minutes for medium.
Lightly toast the buns on the grill. Spread the aioli on the top and bottom buns. Sandwich with the burgers, roasted tomatoes, caramelized onions and arugula.
Photograph by Ryan Dausch
Recipe courtesy of Helena Easterday for Food Network Magazine