- Preheat oven to 300 degrees. In a large pot, heat 1 tablespoon oil over medium-high heat. Meanwhile, pat rabbit haunches dry with paper towel and season generously with Kosher salt and pepper.
- Lightly dust haunches with seasoned flour, shaking off any excess before carefully adding to hot pan. Brown haunches on all sides, making sure not to let any part burn. When evenly browned, remove haunches from pan and let rest on paper towels.
- Carefully remove excess oil from pot and remove any burned flour that may be left. Add tablespoon of fresh oil and add leeks, shallots, and carrots. Season with a pinch of salt and cook 3–4 minutes or until vegetables begin to soften.
- Add garlic, bay leaves, and black peppercorns, and cook 2 more minutes. Add wine, bring to boil, and reduce liquid by half.
- Add rabbit haunches in a single layer, careful not to overlap them. Add stock until it just about covers legs and bring to simmer. Cover pot and put into oven.
- Let braise 1–1½ hours or until haunches are fork tender. Remove from oven and let cool 1 hour.
- Carefully remove legs and place in oven safe container. Strain cooking liquid and place in clean pot. Bring liquid to simmer, skimming off any fat that rises to the top. 8.
- Once reduced by half, add mustard, cream, and tarragon. Using a whisk, add butter one teaspoon at a time, making sure stock does not boil.
- Add legs back to pot and let rest until ready to serve. Season with thyme and serve.