Make the sausage: In a medium bowl, mix together all the sausage ingredients until incorporated. Divide into 6 patties, 1 inch thick.
Step 3
Make the burgers: In a large skillet, heat the olive oil over medium-high heat. Add the peppers, onion and fennel, and cook, stirring often, until soft and caramelized, 20 minutes. Stir in the honey and vinegar, then season with salt and pepper. Remove from the heat and keep warm.
Step 4
Light a grill. Brush the burgers with olive oil and grill, flipping once, until charred and cooked through, about 12 minutes. After flipping, spoon the vegetables over each burger and top each with 1 slice of cheese. Spread Dijon mustard on both sides of the bun and then place the burger on the bottom half. Garnish with a few fennel fronds and top with the other half of the bun, then serve.