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1
MAKE THE CRUST DOUGH IN A FOOD PROCESSOR: Place the flour, sugar, and salt into the food processor and pulse a few times to mix. Add the bits of butter and pulse until the butter is mixed into the flour so that it resembles a coarse meal. Whisk the egg with the ice water and pour into the food processor a little bit at a time, pulsing once after each addition. You don't want to overwork the dough. Pour the dough out onto a counter and roll it into a ball. Again, don't overwork the dough. Now, flatten it with your hands into a small disk; wrap in plastic and chill for at least 3 hours.
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2
SAUTE THE MUSHROOMS: Preheat the oven to 400 degrees. In a large skillet, melt 4 tablespoons of the butter over medium-high heat. When the butter is bubbling and beginning to brown, add the mushrooms and saute. They will release liquid as they cook. Cook until this liquid has evaporated from the pan and the mushrooms begin to brown, about 10 minutes. Add the garlic and saute 1 minute more. Add the white wine and deglaze the pan, scraping up the browned bits as you stir, allowing the wine to evaporate. Season the mushrooms with salt and pepper to taste and remove the pan from the heat.
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3
SAUTE THE LEEKS AND FENNEL: In another large skillet, melt 2 tablespoons of butter and 1 tablespoon olive oil over medium-high heat. When the butter begins to bubble and turn brown, add the fennel, leeks, and shallot. Saute until soft and beginning to brown, about 10-15 minutes. Season to taste with salt and pepper.
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4
ROLL OUT THE DOUGH; FILL IT; AND BAKE: Place the disc of dough between two sheets of wax paper and roll it out into a rough 1/4-inch thick square or circle. A galette is supposed to look rustic, so don't concern yourself too much with the shape. Transfer the dough to a buttered baking sheet. Leaving a 2-inch border, sprinkle the dough with the Fontina cheese. Mix the mushrooms and leek mixture together in one of the skillets. Pour the vegetables into the center of the galette and spread out into an even layer, leaving the 2-inch border. Fold the edges over. Sprinkle the top with Parmesan cheese, olives, and thyme leaves. Place in the center of the oven. Bake until the crust is golden brown, about 25-30 minutes.
