1. Heat oven to 400°F. Use vegetable peeler to peel skin off ginger. Continue using peeler, cutting lengthwise, to make paper-thin slices of ginger. Stack slices and use sharp knife to cut into very thin strips resembling threads.
2. Heat butter in medium saucepan over medium heat until foamy. Stir in 2 to 3 tablespoons ginger threads, star anise and cranberries; sauté until cranberries begin to soften, about 5 minutes.
3. Add enough water to just cover the cranberry mixture. Reduce heat to simmer; cook until cranberries break down, about 7 to 10 minutes. Stir in honey and rosewater; season with salt and pepper to taste. Keep warm.
4. Combine fennel, lemon slices and 1/4 cup olive oil in large baking pan; season with salt and pepper. Roast in 400°F oven until golden and cooked through, 25 to 30 minutes.
5. While the fennel is roasting, heat remaining 2 tablespoons olive oil over high heat in large cast-iron skillet. Season tenderloin with salt and pepper; brown on all sides, about 5 minutes. Transfer skillet to oven and bake for until internal temperature reaches 145°F to 160°F. Let stand 10 minutes before slicing. Place sliced tenderloin and fennel on serving platter; top with cranberry-ginger relish. Garnish with fennel fronds and serve immediately.