Lay rabbit pieces on a sheet of parchment paper and season each piece generously with kosher salt and freshly ground black pepper.
Spread 1 cup flour on a separate sheet of parchment paper and dredge the seasoned rabbit pieces in the flour, shake off excess flour. Reserve about 1 tablespoon of flour to sprinkle over cooked onions.
Heat a medium sized deep sided skillet or Dutch oven over medium-high heat and add 1 tbsp lard or vegetable oil. When the fat is hot, add the rabbit legs in one layer without crowding; work in batches if necessary. Adjust heat to keep them from browning too quickly. Sear for about 3 to 4 minutes on each side until nicely browned.
Remove browned rabbit from pan and set aside. Add 1/2 large yellow onion, diced to the fat remaining in pan. Keep heat on medium high and cook onions until softened and lightly browned, stirring occasionally, about 5 to 6 minutes. Season with kosher salt and freshly ground black pepper.
Sprinkle onions with 1 tablespoon of flour remaining from dredging rabbit pieces and stir until well incorporated, then cook for a minute or so, until mixture starts to smell toasty.
Add 1/2 cup dry white wine and 1 cup chicken stock, stir and bring to a simmer. Taste for seasoning and adjust if necessary.
Return browned rabbit pieces to the sauce. Add 2 sprigs thyme and 6 whole sage leaves. Cover pan, reduce heat to medium low and cook for 45 minutes to an hour, or until meat is fork tender.
Using tongs, remove rabbit pieces from sauce, set aside, and keep warm. Increase heat under saucepan to medium and bring contents to a simmer. Whisk in 1/2 cup crème frîache, 1 tbsp Dijon mustard or grainy mustard, 2 tsp capers and cook until somewhat thickened, about 5 minutes. Taste sauce and adjust.
Using a fork, shred the meat from the bones, discarding the bones. Return shredded rabbit to the pan and stir to combine with the sauce.
Cook pappardelle or fettuccine pasta according to package direction and when cooked, transfer cooked pasta directly from the cooking water to the sauce and stir to combine.
Sprinkle with 1/3 cup thinly sliced fresh chives or fresh parsley and serve.