In a heavy skillet over medium heat warm about 1 to 2 teaspoons olive oil. When hot add in chopped onions and cook until wilted. Stir in minced garlic, basil and oregano. Cook for 1 to 2 minutes. Remove from heat and allow to cool.
In a large mixing bowl combine the ground turkey, sausage and cooled onion mixture. Add fennel fronds and chili sauce to meat. Season with salt and black pepper. Mix only to combine and shape into 4 patties. Allow to rest at room temperature while preparing slaw.
In a medium bowl toss together together the fennel, cabbage and green onions. In a small bowl whisk together the olive oil, vinegar and sugar. Pour over salad ingredients tossing to coat. Season with salt and pepper to taste.
Preheat a heavy skillet or flat griddle over medium high heat. Drizzle the burgers with olive oil and place oiled side down on preheated pan. Cook turning once until cooked through, approximately 5 minutes per side for 3/4 inch patties. When turning drizzle top with olive oil before turning.
When burgers are cooked through turn off heat, top with a slice of cheese. Tent with foil and let stand for 2 minutes. Place burgers on individual serving plates with the slaw, garnish with fennel fronds and enjoy.