Step 1

Place a rack in lower third of oven; preheat to 400°. Toss potato, sweet potato, carrots, parsnip, and onion with oil on a rimmed baking sheet; season with salt and pepper and arrange vegetables in a single layer. Roast until golden around the edges and tender, 30–35 minutes. Let cool.

Step 2

Meanwhile, cook sugar and 2 Tbsp. water in a small saucepan over medium-high heat, swirling pan occasionally, until mixture is amber-colored, 5–7 minutes. Remove from heat and add vinegar and a pinch of salt, swirling pan to combine. Quickly pour caramel into a 9”-diameter pie pan; tilt and rotate pan to evenly coat bottom with caramel. Scatter rosemary and sage over top.

Step 3

Arrange potatoes, carrots, and parsnips snugly in a single layer on top of caramel, using smaller carrot and parsnip pieces to fill in any holes. Scatter onion rings and crumble goat cheese over vegetables.

Step 4

Roll out dough on a lightly floured surface to a 12” round. Drape over vegetables, tucking edges into pan. Prick dough all over with a fork. Bake until crust looks dry, about 20 minutes; reduce heat to 350° and bake until crust is golden brown, 15–20 minutes.

Step 5

Let tart cool 5 minutes before inverting carefully onto a large plate.

Step 6

DO AHEAD: Vegetables can be roasted 4 hours ahead. Keep at room temperature.