Bring four quarts of water and two tablespoons of the salt to a boil in a large pot. If baking right away, place an oven rack in the middle position and heat the oven to 325 degrees Fahrenheit. Coat the bottom and sides of a 9-by 13-inch baking dish with one tablespoon of the oil and set aside. Add the noodles to the boiling water and cook for three minutes less than the low end of the package instructions, stirring occasionally to prevent sticking. Drain and let cool for at least five minutes.

Meanwhile, in a very large bowl, combine the eggs, sour cream, labne, buttermilk, remaining four tablespoons (1/4 cup) of oil, the lemon juice, and the remaining two and a half teaspoons of salt and use an immersion blender to puree the mixture until completely smooth. (Alternatively, blend the ingredients in a blender or food processor and transfer to a very large bowl. You can also whisk vigorously by hand, but the other options yield silkier results.)

Add the noodles to the bowl with the custard mixture and stir well to coat. (It will be very loose and soupy at this point.) Transfer to the prepared dish, scraping out the bowl, and spread into an even layer. (At this point the kugel can sit, covered, at room temperature for up to two hours or be refrigerated for up to 12 hours. If refrigerating, allow the kugel to sit on the counter for one hour to take the chill off before baking, and note that it may take longer to cook.)

Bake until slightly puffed and a paring knife or toothpick inserted near the center of the kugel comes out mostly dry with a few curds or streaks of dairy, 40 to 50 minutes. (The center of the kugel should register 160 to 165 degrees Fahrenheit.) Leaving the kugel on the middle rack, heat the broiler to high and broil until the pieces of pasta sticking up are golden brown, two to four minutes (watch closely while broiling to prevent burning). Let cool for at least 20 minutes before slicing and serving.

While the kugel bakes, make the relish : Peel the persimmons, removing the leaves and any tough pieces around the stem and core, then chop the flesh into half-inch pieces (you should have about two cups).

In a medium saucepan, combine 3/4 cup water, the persimmons, honey, ginger, butter, salt, and pepper and bring to a simmer over medium heat. Simmer, stirring and adjusting the heat as necessary to prevent scorching, until the liquid has thickened and become syrupy and the persimmons are tender but still hold their shape, 15 to 20 minutes. Remove the pan from the heat and stir in the lemon juice and mustard. Serve warm with the kugel. (The relish can be made up to three days in advance; just warm it in a pan or microwave before serving. The relish yields two cups.)