Min Kim's sweet and savory galette gets its signature ribbons using a mandolin but a thick peeler will also work fine here.
PREPARE THE CRUST
Combine flours, cornmeal, and salt in a small bowl and place in freezer while you gather the remaining crust ingredients.
In a food processor, add the flour mix and butter and pulse 8 to 10 times until butterpieces are pea-sized. Dump entire contents onto a flat and smooth work area. Drizzle sourdough starter and 2 tablespoons ice water over the dry ingredients and, using your hand and a pastry or bench knife, form into a dough as quickly as you can, being careful not to overwork or warm the dough too much as the butter will melt. Add 1–2 more tablespoons of water if dough seems too dry. Form into a 6” flat disc and refrigerate for 30 minutes.
After the dough has chilled, return it to a lightly floured surface and roll it out into a roughly 10” long rectangle. Use small amounts of flour as necessary to keep it from sticking to your work surface and rolling pin. Fold the rectangle, letter-style, into thirds. Repeat this 2 to 3 more times using more flour as needed. After your last fold, cut the dough in half and stack on top of each other. Try to smooth the corners into a circle shape and flatten out into a 6” disc again. Cover with plastic wrap and refrigerate for at least 1 hour and up to a day.
PREPARE THE FILLING
Preheat oven to 350º with rack positioned in the middle of the oven. In a small mixing bowl, combine ricotta, feta, and ¼ teaspoon of salt until creamy. Set aside.
Wash and peel squash with a heavy-duty vegetable peeler. Cut the bulbous piece off as close to the seeds as you can. Chop the top piece into roughly 3/4” by 1/2” thick sticks and, using a mandolin slicer, carefully slice into long ribbons until you have about 350g (12oz) of strips. If you don’t have a mandolin slicer, you can use a peeler. Set squash aside.
Place pistachios on a baking sheet and toast in oven for 4 minutes. Transfer to a plate to cool. (Rub pistachios in a dish towel to remove some of the skins, if desired.) Finely chop and set aside.
On the same baking sheet, toss the butternut squash slices with a healthy drizzle of olive oil and ¼ teaspoon salt. Bake for 4 to 5 minutes and gently transfer to a plate to cool, taking care not to break the slices.
ASSEMBLE THE GALETTE
Raise the oven temperature to 375º.
Bring out chilled dough and rest on the counter for 10 minutes; roll dough out to about 12” in diameter, lightly dusting, flipping, and moving the dough in a circle as you go. Transfer the dough to a sheet of parchment paper and finish rolling it out to 13”–14” in diameter.
Spread cheese mixture over crust, leaving 2” of space around the edge. Arrange squash ribbons and prosciutto strips over the cheese mixture. Lay extra strips of prosciutto around the outer edges of the squash.
Carefully fold up edges of the galette dough, forming pleats as you go. If dough has become too soft while arranging the filling, place whole galette in the refrigerator for 20 to 30 minutes to firm up (this will prevent the folded edges from opening up while baking).
Transfer the galette and parchment to a baking sheet, brush edges with egg wash, and bake for 35 to 40 minutes. Cool for 10 minutes, then top with chopped pistachios, crumbled feta, and honey before serving.