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Step 1
Whisk together the oat flour, millet flour, sweet rice flour, tapioca starch, sugar, xanthan gum, and salt in a large bowl.
Step 2
Add the butter and mix with your hands, breaking up the butter until the largest pieces are about the size of an almond.
Step 3
One tablespoon at a time, dribble in the ice water, combining after each addition, until the dough holds together when pinched with your fingers.
Step 4
Knead the dough to bring it together. Dust your surface with millet flour and roll out the dough until it is about 1/2-inch thick, using a pastry scraper to help lift and turn it, dusting with more millet flour to keep it from sticking. Fold the dough into thirds, as you would a letter, then fold it in thirds again the other way. Gently press to the dough into a ball and flatten it. Wrap it in plastic and refrigerate for 30-60 minutes.
Step 5
Optional: Repeat the above folding step once more and chill again for 30-60 minutes. This will improve the flakiness of the crust.
Step 6
Preheat the oven to 400ºF.
Step 7
Cut the dough into eight equal pieces. If using OXO's silicone dough bag, dust the bag or your work surface with millet flour and roll each portion into a 6-inch round circle, until it is just about 1/8-inch thick. Trim the edges to make them round, and stack them on a plate dusting with flour to keep them from sticking. Chill while you prepare the filling.
Step 8
Line a large baking sheet with parchment paper.
Step 9
Toss the strawberries with corn starch, lemon juice, thyme, balsamic vinegar, lemon zest, vanilla bean paste or extract, and salt until evenly combined. Add 1/4 cup sugar and toss.
Step 10
Working quickly, lay a round of dough on the baking sheet and top with approximately a heaping 1/4 cup of the filling, leaving a 1-inch border around the outside.
Step 11
Fold the excess dough on top of the ingredients, creasing and pleating as you go. If it cracks, just press it back together. Repeat with remaining dough, Shuffle the galettes to fit evenly on the prepared baking sheet. Pour any remaining juices from the mixing bowl into the center of each galette.
Step 12
Brush the edges of the folded dough with the beaten egg and sprinkle dough with a little bit of sugar.
Step 13
Bake the galettes on the middle rack until the dough is golden, 35-40 minutes, rotating the pan after 20 minutes
Step 14
Use a spatula to transfer to a wire rack to cool for at least 15 minutes. Brush the tops with whisked honey to glisten up the strawberries. Serve warm or at room temperature with a scoop of vanilla ice cream.