Make the dough: mix the flour and salt, cut in the cold butter until crumbly, then add ice water a tablespoon at a time until it comes together. Shape into a disc, wrap, and chill at least 30 minutes.
Salt the zucchini slices and let them sit 15 minutes, then pat dry. Toss with the olive oil, garlic, basil, chili flakes, salt, and pepper.
Preheat the oven to 375°F and line a baking sheet.
Roll the chilled dough into a circle about 12 inches across and transfer to the sheet.
Crumble half the goat cheese in the center, leaving a 2-inch border. Arrange the zucchini on top and scatter over the remaining goat cheese.
Fold the edges of the dough up over the filling, overlapping to seal. Brush the crust with beaten egg.
Bake for 25 to 30 minutes, until golden and crisp. Garnish with fresh thyme and serve.
Notes
Salting the zucchini is key to a crisp galette. For a vegan version, use vegan butter and cheese and brush with plant milk. Best the day it is made.