For the dough, pulse flour and salt in a food processor to combine. Pulse in butter until no dry flour remains and dough begins to collect in small clumps.
Combine vinegar and ½ cup of ice water in a measuring cup. Pulsing, drizzle in vinegar mixture and pulse just until dough all comes together in 1 big clump.
Divide dough in half. Form each half into a disk, wrap tightly in plastic and refrigerate for at least 2 hours before rolling and baking.
Place a rack in lower third of oven; preheat to 400 F degrees.
Toss root veggies and onions with olive oil, salt, and pepper and arrange in a single layer. Roast until golden around the edge and tender, 30-35min. Let cool.
Meanwhile, melt butter and olive oil on a small saucepan over medium-high heat, until foaming subsides. Add sugar and water, until mixture is amber-colored, 5-7 minute. Add the garlic slices. Remove from heat and add the vinegar and a pinch of salt, swirling the pan to combine.
Quickly brush the garlic caramel glaze mixture onto a 9”-fiamter pie pan, rotating pan event to coat bottom with glaze. Scatter fresh herbs of your choice on top.
Arrange root veggie in a single layer on top of glaze, and scatter any veggies that don’t make it onto that first layer on top of that. Smaller root veggies pieces can be used to fill any holes.
Scatter chopped onion and crumble goat cheese over vegetables.
Roll out dough on a lightly floured surface to a 12” round. Drape over vegetables, tucking edge into pan.
Prick dough all over with a fork. Bake until crust looks dry, about 20 minutes; reduce heat to 350 F degrees and bake until crust is golden brown, 15-20 minutes.
Let tart cool 5 minutes before inverting carefully onto a large plate.