1. Melt butter in heavy large skillet over medium heat. Add sliced fennel bulb and crushed fennel seeds and stir to coat. Sprinkle with salt and pepper. Reduce heat to low, cover, and cook until fennel is tender but not brown, stirring often, about 20 minutes. (Can be made 2 hours ahead. Let stand at room temperature.)
2. Place potatoes in large saucepan. Cover with cold water and bring to boil. Reduce heat to medium and boil until potatoes are tender, about 15 minutes. Drain. Return potatoes to pan; cook over medium heat until no liquid remains. Mash potatoes.
3. Add 1 cup half and half to fennel mixture and bring to simmer. Working in 2 batches, add fennel mixture to potatoes; stir to combine. Season with salt and pepper. (Can be made 2 hours ahead. Let stand at room temperature. Re-warm over medium heat, adding more half and half as needed if dry.)