Butter a 10-inch tart pan with removable bottom; set aside.
Prepare the crust: In a medium bowl, combine flour and 1/2 teaspoon salt. Add 8 tablespoons (1 stick) chilled butter, and combine with fingers or a pastry blender until it has the texture of coarse meal. Add 1/2 cup ice water, and stir just until a dough forms. Form into a disk, and wrap in plastic wrap. Chill for at least 15 minutes.
Heat oven to 375 degrees. On a lightly floured surface, roll out dough to 1/8-inch-thick round. Fit dough into prepared tart pan; trim excess. Line with a parchment paper round, and fill with pie weights. Chill for 15 minutes. Transfer to oven, and bake for 15 minutes. Remove pie weights and parchment paper. Bake for 5 minutes more. Remove from oven, and set aside.
In a large skillet, heat remaining 4 tablespoons butter. Add onions, and cook, stirring frequently, until slightly browned and softened, about 15 minutes. Remove from heat. In a small bowl, combine beaten egg, cream, remaining 1 teaspoon salt, pepper, and nutmeg. Stir in onions.
Sprinkle baked tart shell with cheese. Spread onion mixture evenly over cheese. Bake until set, 35 to 40 minutes. Serve immediately.
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