Make the herbed goat cheese: In a small bowl, combine the goat cheese, chives, 1 teaspoon thyme leaves and a sprinkle of salt and pepper. Stir to blend well.

In another large bowl, combine the butternut squash, onion, olive oil, paprika, remaining 1 teaspoon thyme and a sprinkle of salt and pepper; toss to coat

On a lightly floured pizza peel, roll the dough just under ¼-inch thick, or do it on any surface and then place it on a parchment-paper-lined baking sheet. Dollop the goat-cheese mixture over the top and gently spread, leaving a 2-inch border around the edges.

Arrange the butternut squash and onion in an even layer, as thin as possible on top of the goat cheese. Fold the crust up and over the squash and press gently to seal. Brush the crust with egg then sprinkle with salt and pepper. If the crust is very soft, refrigerate the entire galette for a few minutes until firm.

Preheat oven to 350F and place a pizza stone inside, if available. Bake the galette on the stone until the crust is golden and the squash is cooked through and charring on the edges, 35 to 45 minutes. If the crust is getting too golden before the squash is cooked, tent the galette with foil. Let the galette rest on the baking sheet for about 5 minutes before moving.
Drizzle the filling with balsamic vinegar, if desired.