Make the schmaltz and the broth
Position a rack in the center of the oven and heat the oven to 450°F.
Arrange the chicken wings in a single layer on a rack with a tray beneath to catch the fat. Sprinkle with 1/2 tsp. salt. Roast, flipping once, until the fat from the wings has rendered (this is schmaltz) and the wings are golden brown, about 45 minutes.
Pour the schmaltz into a small bowl to cool; you should have about 2 Tbs.
In a large pot Cover the wings with 3 inches of cool water (about 1 gallon). Bring to a simmer over high heat, scraping up any browned bits from the bottom of the pot. Turn the heat down to low, and cook uncovered, for at least 4 and up to 6 hours.
Add the onion, carrots, bay leaf, peppercorns, and 1 tsp. salt, turn the heat up to medium high, and bring to a simmer. Turn the heat down to low and cook about 1 1/2 hour.
Strain the broth through a fine-mesh strainer into a large bowl, and then strain it again through cheesecloth or heavy-duty paper towels into another bowl. You should have about 8 cups of broth; if you have less, add water to make 8 cups.
Skim any fat that rises to the top of the broth, transfer it to the bowl of schmaltz, and refrigerate until solidified, about 20 minutes.
Make the matzo balls
Combine the matzo meal, eggs, 2 Tbs. of the schmaltz, 2 Tbs. of the broth, the baking powder, 1/2 tsp. salt, and 1/4 tsp. pepper in a medium bowl, gently stirring until thickened, about 1 minute. The mixture should be a sticky paste that holds together but is not heavy or dense; if you need to add more broth to achieve this consistency, add 1 Tbs. at a time, up to 1/4 cup more total. Cover the mixture with plastic wrap and set aside at room temperature for 30 minutes or refrigerate for up to 24 hours.
Using wet hands, very gently form rounded tablespoonfuls of the matzo mixture into 12 1-inch balls, transferring them to a plate. Do not overwork or compress the mixture, or the matzo balls will be dense.
Make the soup
Heat 2 Tbs. schmaltz (or, if you don’t have enough schmaltz, add vegetable oil to make 2 Tbs. of fat) in a 4-quart pot over medium-high heat until shimmering hot. Add the onion, carrots, celery, and 1-1/2 tsp. salt, and cook, stirring occasionally, until the onion is soft and browned at the edges, about 6 minutes. Add the remaining broth and bring to a simmer. Season to taste with salt, if necessary.
With wet hands, add the matzo balls to the soup and return it to a simmer. Turn the heat down to low, cover, and simmer until the matzo balls are cooked through and doubled in size, about 30 minutes (no need to turn them). Insert a toothpick into the center of a matzo ball and if it slides in and out without resistance, they’re done. Serve the soup garnished with the parsley.