Take your butter and cut it into about ½" pieces. Place in a small bowl and put in the freezer for at least 30 minutes.
Mix together flour and salt in a medium-large bowl.
Dump frozen butter into flour mixture. Using a pastry cutter, cut butter into flour until it is about pea size bits.
Add 1 tbsp of vodka and 4 tbsp of ice water. Mix until dough comes together, adding extra tbsp of water if needed. Dough should come together but not be wet.
Pat dough into a 5-6" disc and wrap in plastic wrap. Place in the refrigerator for at least 4 hours.
After about 3.5 hours, or about 30-45 minutes before you take your chilled dough out, slice your zucchini into ⅛ inch slices. Lay the slices in an even layer on paper towel and lightly salt.
Allow the zucchini to sweat for about 30 minutes. Blot with a paper towel before they go onto the galette.
Preheat oven to 375°F
When dough has sufficiently chilled, take out and place on a floured parchment sheet. Roll dough out until about ⅛" thick. Dough should be mostly round but does not need to be perfect.
Slide your parchment sheet with dough onto a baking sheet.
Spread your goat cheese over the center of the dough, leaving a 1-2 inch border around the edges.
Arrange your zucchini slices over the goat cheese in whichever design is the most pleasing to you. I find rows or circular to be the easiest.
Take a piece of the edge and fold over, towards the center. Take the section next to it and repeat around until your galette has a crust.
Lightly brush the zucchini with olive oil. If you have olive oil cooking spray, this will work too. Brush the crust with beaten egg, and sprinkle with flaky sea salt.
Bake on center rack of oven for about 45-55 minutes, until crust is golden brown and zucchini is starting to be browned.
Remove from oven and allow to cool slightly before serving. Enjoy!
