Position a rack in the upper third of the oven and preheat to 475 degrees F. Fill a bowl with hot water; add the noodles and soak 10 minutes. Drain and hang side by side over the bowl's edge so the noodles don't stick. Meanwhile, mince the shallot in a food processor. Heat a skillet over medium-high heat. Add the shallot and 1 cup broth; cook 3 minutes. Add the flour and nutmeg; whisk until smooth, 1 minute. Whisk in the remaining 2 cups broth; cook, whisking, until thickened, 7 minutes. Whisk in 1/4 cup ricotta and the parsley; remove from the heat. The sauce will look textured from the cheese. Mince the celery and carrots in the food processor. Add the remaining 3/4 cup ricotta, 1/2 cup mozzarella and the egg; pulse until smooth. Spread 2 tablespoons of the shallot sauce in a 9-by-13-inch baking dish. Top with 3 noodles and half of the mozzarella mixture. Repeat the layers, ending with noodles. Top with the remaining shallot sauce, the tomatoes and the remaining 1/2 cup mozzarella. Bake until bubbly, about 20 minutes.