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To make the crust: In the bowl of a food processor fitted with the blade attachment, combine the flour and salt. Pulse several times to combine.
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Add the butter and cream cheese and pulse 6 to 10 times, until the mixture is evenly crumbly, with pieces of butter and cream cheese no larger than the size of peas.
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Drizzle in the water and pulse until evenly moistened and the dough begins to gather into one mass, 10 to 15 pulses.
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Transfer the dough to a piece of plastic wrap or your favorite reusable wrap. Use the wrap to gather the dough into a mound and press it into a cohesive disk about 6" in diameter and 3/4" thick. Wrap tightly and chill in the refrigerator for at least 1 hour and up to 2 days in advance. (The cream cheese keeps the dough firm but pliable, so there’s no need to let the dough warm up before rolling.)
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To make the filling: In a large bowl, use a flexible spatula or sturdy spoon to mix together the cream cheese, mayonnaise, grated garlic, salt, pepper, and ground mustard.
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Roughly chop half (240g) the artichokes, then add them to the cream cheese mixture along with the spinach, mozzarella, and Parmesan. Stir to combine and continue mixing until the spinach and artichokes are evenly distributed. Cover and refrigerate until ready to bake, up to 1 day in advance.
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To assemble and bake: Preheat the oven to 425°F with a rack in the lower third of the oven. Line a rimmed baking sheet with parchment.
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Remove the crust dough from the refrigerator and place it on a lightly floured surface. Use a rolling pin to roll the dough to a 14" round that’s about 1/8" thick, dusting the surface with flour as needed to prevent sticking. Transfer the round to the parchment-lined baking sheet. (It will overhang the edges of the pan slightly at this point; that’s OK.)
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Remove the filling from the refrigerator and spread it over the dough in an even layer, leaving a 2" border around the edges bare.
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Arrange the reserved artichokes, cut-side up, on top of the filling in a decorative pattern. Fold the edges of the dough up over the filling, leaving the center uncovered. Brush the top of the dough with heavy cream, half-and-half, or milk.
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Bake the galette for 50 to 55 minutes, until the crust is golden brown. Remove from the oven and let cool slightly on the baking sheet for 5 minutes. Slice and serve the galette while warm.
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Storage information: Store leftover Spinach Artichoke Galette in an airtight container in the refrigerator for up to 4 days. To reheat, place slices of the galette on a foil-lined baking sheet. Warm in a preheated 350°F oven until hot, 10 to 15 minutes.