Using a handheld slicer, slice potatoes, beets, fennel, and radishes into 1/8-in.-thick slices. Preheat oven to 325°.
Put butter, shallots, and garlic in a small saucepan and cook over medium-low heat until aromatic, about 1 minute. In a small bowl, whisk 2 tbsp. flour with 1/4 cup cream until smooth. Whisk in remaining cream, then pour into saucepan along with 1 tbsp. thyme, the rosemary, salt, and pepper; let simmer until shallots are translucent, about 5 minutes.
Butter a 1- to 1 1/2-qt. ceramic or cast-iron gratin dish or shallow baking dish. Arrange half of potatoes, beets, radishes, and fennel slices tightly to cover bottom of dish, overlapping them like dominos and alternating vegetable types, in an oval around edges and a row up center. (You may have to tuck fennel pieces in since slices may not hold together.) Season lightly with salt and pepper. Pour half of cream mixture over slices, stirring as you pour so shallots and garlic are evenly distributed, and top with half of Gruyère. Arrange remaining sliced vegetables the same way, then top with remaining cream mixture and Gruyère. Sprinkle parmesan on top.
Cover gratin with oiled foil and bake until vegetables are tender when pierced with a fork, 1 to 1 1/2 hours. Remove the foil and broil until golden and bubbly, about 5 minutes.
Top with remaining 1 tbsp. thyme. Let sit 10 minutes before serving.