Preheat oven to 375°F (190°C). Grease a 9-inch (23-cm) baking dish with butter or cooking spray.
Peel and slice potatoes into thin ¼–⅓-inch (6–8 mm) slices. Place in a large bowl, add the thyme and rosemary, and season generously with salt and pepper. Set aside.
Peel and slice turnips, onion, carrots, and fennel into thin ¼–⅓-inch (6–8 mm) slices. Place in the same bowl as the potatoes.
Add the flour to the bowl with the vegetables and mix until all pieces are evenly coated with flour.
Pour heavy cream over the vegetables and mix until completely combined.
Transfer the vegetable mixture to the prepared baking dish. Sprinkle the top with Asiago cheese and reserved fennel fronds, then season lightly with additional salt and pepper.
Bake in preheated oven for 40–45 minutes or until golden brown on top. Let cool slightly before serving.