Cut cold butter into small (about 1 Tbsp-sized) pieces and set aside.
In food processor, pulse together flour, cornstarch, sugar and salt.
Sprinkle your butter over the mixture, cover, and pulse until mixture forms fine crumbs
Add water, about 1 Tbsp at a time until dough begins to cling together (you may need an additional Tbsp of water).
Pour crumby dough onto parchment paper and press together using the palm of your hand (flattening the crumbs and pressing together). Fold dough over onto itself and then repeat the process of flattening the dough with the palm of your hand (this helps create a flakier crust).
Divide into 8 equal-sized pieces (about ¼ cup each), roll each into a ball, slightly flatten into a disk, and tightly wrap with clear wrap.
Transfer to refrigerator and chill for at least one hour. Prepare your peach mixture while you wait for the dough to chill.
Peach Filling
In a large bowl, combine your peach slices, sugar, cornstarch and lemon juice. Stir until completely combined. Allow to set for at least 30 minutes (you may stir the mixture periodically).
Cheesecake Layer
To prepare your cheesecake, stir together cream cheese and powdered sugar.
Stir in egg yolk and vanilla extract until all ingredients are well-combined. Set aside.
Preheat oven to 400F
(if galette crust has been refrigerated for longer than one hour, you may need to let the dough sit at room temperature for 10 minutes before it can be easily rolled out).
On a clean, lightly floured surface using a lightly floured rolling pin, roll each ball of galette dough into approximately a 5-6" circle. Transfer to prepared cookie sheet and evenly divide cheesecake mixture among galettes, spreading the filling over the crust and up to ½" from the edges.
Use a slotted spoon to drain spoonfuls of the peach mixture, and then layer the drained peaches over the cream cheese filling. Discard any extra juice.
Gently fold the crust over the edges of the peaches and cream cheese layer to form the rustic edges of the galettes.
Brush crust with lightly beaten egg and sprinkle generously with sugar.
Bake on 400F for 25-30 minutes.
Allow to cool before serving. Serve topped with vanilla ice cream, if desired.