Season rabbit pieces with salt and pepper.
Melt butter in a large skillet over medium-high heat. Brown rabbit pieces on all sides, about 8–10 minutes. Remove and set aside.
Add onion and garlic to the skillet, cooking 4–5 minutes until softened.
Add broth, scraping up any browned bits from the bottom of the pan.
Return rabbit to the skillet, cover, and simmer 35–40 minutes until tender.
Remove rabbit. Temper sour cream with a ladle of hot liquid, then whisk it into the skillet along with mustard.
Return rabbit to the sauce and warm through without boiling.
Top with fresh dill and serve.