Everyone likes potatoes, but this is a good way to introduce fennel to those who are unfamiliar with its singular flavor. Unlike many potato gratins, this version uses chicken stock instead of cream, so it's much less fattening - but we think you'll like the fresh flavors of this dish so much that you won't miss it!
Heat the oil in a large skillet over medium heat and add the fennel. Cook, stirring frequently, until the fennel softens and begins to turn golden, about 10 minutes. Add the garlic, salt, and pepper to taste and cook, stirring continuously, for 2 minutes or until the garlic is fragrant. Don't allow the garlic to burn.
Add 1/4 cup of the chicken stock and the vermouth to the skillet, cover the pan, and cook over medium-low heat until the fennel is tender, 5 to 8 minutes. Remove the cover and stir in the fennel pollen, if using.
Position a rack in the middle of the oven and preheat the oven to 375 degrees F. Transfer the fennel to a 7x11-inch baking pan.
Arrange the potato slices atop the fennel, overlapping the slices. Season the potatoes with salt and pepper to taste. Pour the remaining chicken stock into the pan; it won't cover the potatoes. Tightly cover the pan with a piece of aluminum foil. Bake for 50 minutes, then remove the foil. Sprinkle the parmesan cheese over the top of the potatoes and return the pan to the oven. Bake until the cheese has melted and the potatoes are tender, 10 to 15 minutes more. If the cheese doesn't brown, run the dish under a broiler for a few minutes to gratinée.
Let cool for 5 to 10 minutes before cutting and serving.