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1
Preheat oven to 350 degrees F (175 degrees C).
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2
Mix crushed crackers and melted butter together in a bowl; press into the bottom and up the sides of a 9-inch springform pan.
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3
Bake in the preheated oven for 10 minutes. Remove crust from oven and brush egg white onto the crust, to seal. Bake 4 minutes more. Remove from oven and cool to room temperature.
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4
Season chicken with salt and pepper.
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5
Heat olive oil in a heavy large skillet over medium heat; cook and stir chicken just until brown, about 2 minutes per side. Transfer chicken to a plate.
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6
Reduce heat under skillet to medium-low; add 2 tablespoons butter. Cook and stir shallot in the hot butter until beginning to soften, about 2 minutes. Add mushrooms, garlic, rosemary, and 1 pinch salt; cook and stir until mushrooms are tender and juices evaporate, about 8 minutes.
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7
Whisk cream, eggs, 1/4 cup grated Parmesan cheese, 2 tablespoons parsley, 1/2 teaspoon salt, and 1/2 teaspoon pepper together in a bowl.
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8
Place baked crust on a baking sheet; top with chicken and mushrooms. Pour egg mixture over top. Sprinkle remaining 2 tablespoons Parmesan cheese over the top.
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9
Bake in the preheated oven until top is lightly golden and middle is set, 30 to 35 minutes. Let tart rest for 10 minutes. Remove outer ring. Top tart with 2 tablespoons remaining parsley.
