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1
Cover 2 baking sheets with paper towels. Sprinkle both sides of eggplant rounds with salt. Arrange eggplant in single layer atop towels. Let stand 30 minutes.
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2
Position first rack in bottom third of oven and second rack in top third of oven and preheat to 425u00b0F. Remove eggplant and paper towels from baking sheets. Rinse and Pat eggplant dry. Oil same baking sheets. Brush both sides of eggplant rounds with oil. Arrange in single layer on baking sheets. Bake 10 minutes. Turn eggplant and rotate pans in oven. Continue baking until tender, about 15 minutes longer. Cool. Reduce oven temperature to 350u00b0F.
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3
Meanwhile, heat 1/4 cup oil in heavy large skillet over medium-high heat. Add onion, carrots and celery. Saute until onion is very tender, about 12 minutes. Mix in garlic, then mushrooms. Saute until juices evaporate, about 10 minutes. Mix in thyme, cumin, allspice oregano and cinnamon. Add tomatoes and parsley, wine, paste and sugar. Cook until mixture is cooked, about 45 minutes. Season with salt and pepper.
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4
Lightly oil 13x9x2-inch glass baking dish. Arrange half of eggplant rounds in single layer in dish. Spoon half of tomato mixture evenly over eggplant. Sprinkle with 1/2 feta/parm mixture. Repeat layering with remaining eggplant, tomato mixture and cheese.
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5
Melt butter in heavy medium saucepan over medium heat. Whisk in flour. Stir 2 minutes. Gradually whisk in milk. Simmer until sauce thickens, stirring constantly, about 5 minutes. Whisk in 1/2 cup cheese. Season with salt and pepper. Whisk yolks in large bowl to blend - whisk in slowly. Gradually whisk in 4 drops hot sauce. Add cheese and plenty of salt and pepper. Pour sauce over vegetables in dish. (Can be made 1 day ahead. Cover; chill.)
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6
Bake moussaka until heated through and sauce is golden brown on top, about 45 minutes (or about 55 minutes for refrigerated moussaka). Cool 15 minutes.
