Pour 1 tablespoon of vinegar into a ½ cup measuring cup. Fill the remainder of the cup with water and place into the freezer to chill. You’ll want it to remain liquid, so don’t do this too far in advance.
In a large bowl, combine flour, sugar and salt with a whisk.
Remove butter from fridge and cut into 8 pieces, working quickly to avoid warming the butter. Add to the flour mixture and toss to coat butter pieces. Using a pastry blender, cut the butter into the flour until it is pea-sized.
Add the water vinegar mixture. Using a bench scraper or a heavy spatula or wooden spoon, push the mixture back and forth until the liquid has been absorbed into the dry ingredients. Using your hands, lift the edges of the rough dough mass, turn them inwards and press them firmly down. Repeat this, turning the bowl, until you can gather the dough into a rough ball, and there are no loose pieces at the bottom of the bowl.
Place the dough onto a lightly floured work surface. Form into a flattened rectangle and wrap well with plastic wrap. Place in refrigerator to chill for several hours.
Once chilled, place rectangle of dough on a lightly floured work surface. Holding a rolling pin at one end, pound the dough with about four or five vigorous whacks while moving from left to right. Rotate the dough 180 degrees and pound it again.
Roll the dough out until it is somewhat larger and flatter, working to maintain the rectangular shape. With the long edge closest to you, fold the dough into thirds (as with a letter) by lifting the right edge and folding it ⅔ of the way across, and then folding the left edge over until it touches the right edge. Flip the dough over and pound the dough with the rolling pin again.
Roll the dough out by placing the rolling pin in the center of the rectangle and firmly pressing down while moving the pin towards the outer edge of the dough. Turn the dough clockwise 90 degrees and continue this process of rolling and turning until the dough forms a rectangle slightly less than 13 x 18 inches in diameter (the dimensions of a standard half-sheet baking pan in the US) and about ⅛ inch thick. Trim dough if needed with a knife to achieve these dimensions.
Line a half-sheet baking pan (13 x 18) with parchment paper. Gently fold the dough in half and lift it onto the pan. Center it carefully and unfold it. Cover with plastic wrap and place into the fridge to chill.
CORNMEAL FRANGIPANE
In the bowl of a food processor, add the sugar, cornmeal, almond flour, all purpose flour, vanilla, almond extract and eggs. Scatter the butter over the top. Process until well mixed. You may need to stop the processor to scrape down the sides partway through. Use an offset spatula to smooth the filling evenly over the galette dough, leaving bare a one inch border of dough around the edges.
PEACH TOPPING
Cut peaches in half and remove pits. Slice each half from top to bottom into 6 roughly even wedges (do this easily by cutting each half into two quarters, and then cutting each quarter into three). Starting at one corner, arrange peaches on top of frangipane in shingled (slightly overlapping) groups of three, alternating the direction of each neighboring group of peaches to create a rough basket-weave pattern (see photos for reference).
Fold edges of galette dough in about 1 inch, working your way completely around the galette. Press dough gently at corners to seal the folds and prevent the crust from unfolding while baking. Place unbaked galette in fridge for at least 30 minutes to chill.
Immediagely prior to baking, brush the crust with the beaten egg and sprinkle crust and peach filling generously with turbinado sugar.
Bake on center rack at 400 degrees F (200 C gas number 6) for 30 minutes. Reduce temperature to 350 degrees (177 C, gas number 4) and bake an additional 35-40 minutes, until crust is golden brown and peach juices begin to bubble. If the crust begins to brown before the galette is finished, cover just the crust portion with strips of aluminum foil.
Place on a cooling rack until just warm to the touch. Cut into slices and serve!White wine and late summer sunshine are optional accompaniments, but either or both are highly recommended.