A part of the inspiration for the name of this site, this dish is a mash-up of dumplings from a knoephla soup recipe and the tomato sauce from an old Cook's Illustrated recipe ($). I botched the polenta, but the sauce was a winner.
Feel free to use any tomato sauce you like. Something rustic and hearty is what this aims for, but use whatever's in your pantry if you want to keep it simpler.
In a medium bowl, stir together all the ingredients for the knoephlas until it forms a stiff dough. Set a dish towel over the top of the bowl and set it aside.
Put a (3qt or so) pot of water on to boil.
In another pan (~2qt), prehead the fat for the sauce over medium-ish heat. Add the onion, carrot, and celery and sweat until soft and translucent. Add the tomatoes, stir, and leave to simmer gently, stirring occasionally, while you work on the dumplings.
Remove the knoephla dough from the bowl to the counter and knead briefly. Cut off hunks of dough small enough to work with and roll into a rope approximately about the diameter of a finger and cut into bite-sized pieces.
Salt the now-boiling water well. Then, working in batches, boil the knoephlas until they are floating and cooked through. Evacuate each batch to a bowl.
Meanwhile, preheat a 12" nonstick skillet with about a few tablespoons of fat. After the first couple batches of knoephlas are boiled, add them to the pan. As you finish more batches, transfer them into the skillet, spreading into a single layer (or as close to that as possible).
When the first side is golden brown, stir/flip the knoephlas to brown another side. Continue to brown on as many sides as you have the patience to wait for. When nearly finished, season generously with salt and black pepper to taste.
At this point, you may want to scoop out some of the crispy knoephlas and set them aside. They are delicious on their own.
Spoon tomato sauce into the skillet with the remaining knoephlas and stir/toss them together until evenly coated. Add as much sauce as you need to get your preferred level of sauciness. I serve mine relatively dry, so most of the sauce is absorbed into the dumplings.
Serve as is, or with parmesan cheese, red pepper flakes, or other pasta-style accompaniments.