Season the rabbit with salt and pepper. Spread about half of the Dijon over all sides.
Dredge the coated pieces lightly in flour and shake off any excess.
Heat olive oil and butter in a wide pan over medium-high. Brown rabbit well on both sides, then set aside.
Lower heat to medium. Soften shallots in the same pan, then stir in garlic for 30 seconds.
Deglaze with white wine, scraping up browned bits, and reduce by about half.
Add broth, thyme, and bay. Return rabbit to the pan. Cover and simmer gently until tender, 30–35 minutes.
Stir in heavy cream, remaining Dijon, and whole-grain mustard. Simmer uncovered until the sauce thickens, 6–8 minutes.
Taste and adjust seasoning. Sprinkle with parsley and rest 5 minutes before serving.