Pulse the dry ingredients together in a food processor or mix with hands. Add in the yogurt, followed by the butter (use a pastry cutter if no food processor), then the water. Form into a flattened disc and pop in the fridge for 30min to an hour.
Once it's chilled, preheat your oven to 375 degrees F.
Gently roll it out on a piece of parchment into a large circle about 1/4 in thick. It will not be sturdy since it's gluten free, so be careful with it's delicate nature. Transfer to a baking sheet.
Spread some goat cheese down in a circle (not all the way to the edge), followed by thinly sliced tomatoes. Top with hefty amount of sea salt, freshly ground pepper, and more thyme. Drizzle on some garlic infused olive oil.
Fold over the edges and give them an egg wash.
Bake in the oven for about 40 minutes. Serve warm or cold!