Heat a pan with the tablespoon of olive oil to medium-high heat. Add the pecans and toast, stirring frequently, until browned and fragrant. Remove from the heat and sprinkle lightly with salt.
Remove the stalks from the fennel and reserve the fronds. Peel away any fibrous outer layers of the bulb. Cut the fennel into very thin slices (1/8") with a sharp knife or a mandoline. Combine the fennel slices with the fronds in a large bowl.
Peel and segment the grapefruit over the bowl so the juices will dress the fennel. After you've segmented it, squeeze out any juices from the remaining grapefruit pulp into the bowl.
Add the dates, olive oil, and salt and pepper to taste. Sprinkle with parmesan and pecans and toss well to coat.