In a large bowl or food processor, combine flour and salt.
Work in the butter, being careful to not overmix. The texture should be like pea-sized bits.
Add in the sourdough starter and honey, then stir until just combined.
Roll into a ball and cover with a towel. Allow to ferment in a warm place for at least 8 hours and up to 24 hours.
After the dough has fermented, divide into two, roll into balls, and refrigerate for a few hours.
Place in the fridge to chill until time to roll it out.
Preheat the oven to 400 degrees.
Chop the leeks and use only the white and light green parts. Wash in a bowl of cool water and allow to drain and dry.
In a pan over medium heat, add 1⁄2 tbsp of olive oil and cook the leeks until they have softened. Season with a pinch of salt.
Transfer to a plate while you prepare the rest of the ingredients.
In a small bowl, stir heavy cream, goat cheese, lemon zest, and a pinch of salt together.
Thinly slice a small, peeled sweet potato and set aside the slices.
On a lightly floured surface, roll out pie dough to roughly a 12-inch circle.
Prepare a sheet tray (with a raised edge) with parchment paper and arrange the dough carefully on it.
Using the back of a spoon, spread the goat cheese and cream mixture over the dough, leaving a 1” border.
Top with a thin layer of sweet potato slices and lightly drizzle with olive oil.
Sprinkle chopped sage evenly over the potato slices, and scatter the cooked leeks over the top. Fold the edges of the dough over the filling.
With a pastry brush, lightly brush the top of the dough with some cream to achieve browning in the oven.
Bake at 400 degrees for 35-45 minutes, until the crust is golden brown.
When the galette comes out of the oven, drizzle with honey and fresh thyme. Sprinkle with a bit of coarse salt, if desired.