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Pulse 2 cups flour and 1¼ teaspoons salt in food processor to combine. Add butter and pulse until mixture resembles coarse meal with a few pea-size pieces of butter remaining.
Transfer mixture to a large bowl; drizzle with vinegar and ¼ cup ice water. Mix with a fork, adding more ice water by the tablespoonful as needed, just until a shaggy dough comes together. Place dough on a work surface and lightly knead until no dry spots remain (be careful not to overwork). Pat into a disk and wrap. Chill at least 2 hours.
Heat a drizzle of olive oil in a pan over medium heat. Add cabbage and season generously with sea salt. Sauté 5 minutes, until cabbage is soft.
Unwrap dough and roll out on a lightly floured sheet of parchment paper to a 14" round about ⅛" thick. Transfer parchment and dough to a baking sheet. Spread sautéed cabbage over dough, leaving a 1½" border. Arrange sweet potato slices over cabbage, slightly overlapping. Bring edges of dough up and over filling, overlapping as needed to create a 1½" border; brush dough with egg. Sprinkle sweet potatoes with sea salt and pepper and drizzle with olive oil. Chill in freezer 10 minutes.
Bake galette 55–65 minutes, rotating once, until crust is golden brown and cooked through. Let cool slightly on baking sheet before slicing and serving.
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