Pulse together the Pamela's All-Purpose Flour, sugar, xanthan gum, and salt in the bowl of a food processor. (If you don't have a food processor, you can whisk by hand).

Add the cold butter, but don't pulse. One tablespoon at a time, dribble ice water into the food processor, pulsing after each addition, until the dough holds together when pinched with your fingers. Add water until it just holds together, but is not sticky. If you need more water, add a teaspoon at a time. (If working by hand, mix the butter into the flour with your hands, breaking up the butter until the largest pieces are about the size of a pea. Mix in ice water, one tablespoon at a time, until the dough just holds together).

Form the dough into a flat disc and wrap in plastic. Refrigerate for 30 minutes to an hour.

Meanwhile, prepare the filling as directed below.

On a lightly floured surface, roll out the dough to ⅛-inch thickness. Use a 4-inch cutter to cut dough rounds and transfer each round to a large parchment-lined baking sheet. Roll out the scraps and repeat until you have 10 dough rounds.

Preheat the oven to 400°F.

Spread the kabocha squash cubes on a large parchment-lined baking sheet and toss with olive oil and about ¼ teaspoon each of salt & pepper. Bake for about 15 minutes, until just tender when pierced with a fork. Place the cooked squash in the refrigerator to cool before filling the empanadas.

When the dough rounds are ready, place filling components in the following on one half of the round: about 1 teaspoon of shredded gruyère, 1 tablespoon cooked kabocha squash, 1 teaspoon chopped shallot, a pinch of minced garlic, and leaves from half a sprig of thyme. Sprinkle with salt and pepper.

Prepare the egg wash by whisking the egg and water together in a small bowl.

Lightly brush the edge of one half of one dough round with the egg wash, fold the round in half around the filling, lightly crimping the edges together with your fingertips. Repeat with all 10 empanadas.

Brush the egg wash over the top of each empanada.

Bake your empanadas for 30-35 minutes rotating the baking sheet halfway through, until the tops are lightly golden brown. (Tip: Keep an eye on your empanadas after 20 minutes, as the color of your baking sheet can vary the baking time!).

Serve warm.