Chill a medium-size platter for at least 20 minutes.
Toss fennel in a small bowl with a drizzle of olive oil, pinch of salt, and squeeze of lemon juice. Scatter in an even layer on chilled platter, followed by some shaved cheese and a few grinds of black pepper.
Arrange grapefruit pieces over fennel and drizzle more olive oil over the top, followed by another scattering of cheese and black pepper. Toss endive and tarragon leaves in the same bowl with a drizzle of olive oil, pinch of salt, and squeeze of lemon juice, and layer over top of salad.
Finish with remaining cheese, a final drizzle of olive oil, and salt and black pepper to taste.