Season rabbit pieces with salt, pepper, and smoked paprika.
Heat avocado oil in a heavy skillet over medium-high heat. Sear rabbit pieces 3–4 minutes per side, until browned. Remove and set aside.
Add onion to the skillet and cook 8–10 minutes, until caramelized. Add garlic and cook 1 minute more.
Pour in broth, scraping up browned bits, then whisk in xanthan gum to lightly thicken.
Return rabbit to the skillet, cover, and simmer 35–40 minutes, until tender.
Serve smothered in gravy.