How to Make It
Prepare the Dough: Pulse all-purpose flour, rye flour, salt, and sugar in a food processor to combine, 3 to 4 pulses. Add butter, and pulse about 5 times until pea-sized pieces form. Slowly pulse apple cider vinegar, and then ice water by the tablespoon until a rough dough comes together. Form into a 1-inch disk, and cover tightly with plastic wrap. Chill about an hour.
Prepare the Galette: Preheat oven to 350°F. Line a large sheet tray with parchment paper.
Carefully slice all root vegetables into 1/16 inch slices with a sharp knife or a mandoline slicer, and place in a large bowl. Drizzle with olive oil, and sprinkle with kosher salt and pepper.
Stir together cheese, chopped shallot, thyme, heavy cream, and lemon zest in a small bowl until spreadable.
Roll out Dough to about a 14-inch circle (rough edges are fine).Transfer dough to prepared sheet tray. Spread cheese mixture over dough, leaving a 1 1/2-inch border. Layer vegetables to edge of cheese layer. Fold edges of dough up and over top of vegetables.
Bake in preheated oven until vegetables are tender and crust is browned, 55 to 60 minutes. Remove from oven, cover with aluminum foil, and let stand 15 minutes before slicing. Drizzle with extra-virgin olive oil, and sprinkle with flaky salt.