Preheat the oven and prepare the berries - Preheat the oven to 375°F (190°C) and line a baking sheet with parchment paper. Rinse and pat dry the berries, then hull and quarter the strawberries, and leave the raspberries and blueberries whole. Place the berries in a large mixing bowl.
Make the pastry dough - In a food processor, combine the flour and sugar. Add the cold, cubed butter and pulse until the mixture resembles coarse crumbs. Slowly add the ice water, 1 tablespoon at a time, pulsing until the dough comes together in a ball. Remove the dough from the food processor and shape it into a disk. Wrap the disk in plastic wrap and refrigerate for at least 30 minutes or up to 2 days.
Prepare the herb sauce - In a small bowl, whisk together the olive oil, minced garlic, and fresh thyme leaves. Set aside until ready to use.
Roll out the pastry - On a lightly floured surface, roll out the pastry dough into a 12-inch (30 cm) circle. Transfer the dough to the prepared baking sheet.
Add the herbed goat cheese and berries - Crumble the herbed goat cheese onto the pastry dough, leaving a 2-inch (5 cm) border around the edges. Add the prepared berries on top of the goat cheese, spreading them out evenly. Fold the edges of the pastry dough up and over the berries, pleating as needed to make it fit.
Bake and serve the galette - Bake the galette for 35-40 minutes, or until the pastry is golden brown and the berries are bubbling. Remove the galette from the oven and let it cool for 10 minutes. Serve warm or at room temperature, drizzled with the herb sauce.