Dough can be made 5 days ahead. Keep chilled. Let stand at room temperature for 30 minutes before continuing.
Place fennel seeds in a resealable plastic freezer bag. Coarsely crush with a rolling pin or the bottom of a skillet. Alternatively, pulse in a spice mill until coarsely crushed. Transfer to a small bowl; stir in sea salt. Set fennel salt aside.
Arrange a rack in center of oven and preheat to 180°. Line a baking sheet with baking paper. Remove plastic wrap from dough. Roll out dough on a lightly floured surface. Cut out desired shapes. Brush cookies generously with oil, then sprinkle with fennel salt.
Bake, rotating sheet halfway through, until cookies are golden brown (flecks of cheese will be slightly darker), 14–16 minutes. Let cool on sheets for at least 10 minutes. Serve warm or at room temperature.