Cut the butter into 1/2" cubes and put in the freezer for a few minutes. In a large bowl, combine the flour, sugar, and salt.
Add the cubed butter, and with clean dry hands cover the cubes of cold butter with flour. Then pinch the butter into the flour (or use a pastry blender), flattening the butter and making very rough and coarse crumbs (you could also use a food processor for this step).You want to keep the butter mixture cold as you are doing this. If the mixture gets too sticky, put it in the freezer for a couple minutes.
Add the sourdough discard to the butter mixture, combining well with a spoon. Stir only to combine, and do not overwork the dough. If the pastry dough is too dry, add drops of ice water a few drops at a time until the crust holds together.
Lay a piece of parchment paper or plastic wrap onto your counter and dump the dough onto the parchment and work it into a round thick disc.
Fold up the parchment or plastic wrap around the disc, and chill it in the fridge for a minimum of 30 minutes.
Prepare the Filling:
In a medium bowl, toss the sliced strawberries with maple syrup, lemon juice, lemon zest, vanilla extract, and a pinch of sea salt.
Let the mixture sit for 10-15 minutes to allow the juices to release.
Sprinkle the cornstarch (or arrowroot powder) over the strawberry mixture and gently stir to combine, ensuring the fruit is coated evenly.
Add the chopped basil (if using) and stir gently.
Assemble the Galette:
Preheat the oven to 375°F (190°C).
Roll out the chilled dough on a lightly floured surface or a piece of parchment paper to a rough 12-inch circle. If using parchment, it is easier if you place a second piece of parchment on the top to help while rolling. If the dough gets sticky, place it in the freezer for a few minutes.
Transfer the dough (and parchment) onto a baking sheet.
With a slotted spoon, scoop the strawberry-basil filling into the center of the dough, leaving about a 2-inch border around the edges. Discard the liquid.
Fold the edges of the dough over the filling, pleating as you go. The center will remain open, showing the fruit.
Brush the edges of the crust with the beaten egg and sprinkle a little coconut sugar or coarse sugar on top for a golden finish.
Bake:
Bake for 35-40 minutes, or until the crust is golden brown and the filling is bubbling.
Let the galette cool slightly before slicing. The filling will thicken as it cools.
Notes
Be sure to leave a 2-inch border when adding your fruit filling to the sourdough pastry crust. This border will be folded up around the filling.
Fresh fruit will work best in this recipe. Ripe peaches, strawberries, or blueberries would all be great to try.
Adjust the maple syrup or honey based on the sweetness of your strawberries. Early-season berries may need more, while peak-season fruit is naturally sweeter.
Swap basil for fresh mint for a different herbal note.
Ensure the butter remains cold when mixing. If it softens, refrigerate the dough briefly before rolling.
To prevent a soggy crust, use a slotted spoon to scoop the filling, leaving excess liquid behind. You can also sprinkle a thin layer of ground nuts or breadcrumbs on the dough before adding the filling.