Preheat the oven to 350°F (180°C).
1 Wash and cut the fennel into thick slices.
2 Heat the frying pan with butter on low, and cook the sliced fennel with thyme for 5 minutes on each side. If necessary, cook it in several batches.
3 Add the brown sugar and cook until caramelized, for 10 minutes.
4 Remove from heat and spread the puff pastry dough over the fennel, folding the dough inwards.
5 Bake for 30 minutes. Add pepper before serving, and, if desired, shavings of Parmesan cheese.