Season venison generously with salt and pepper.
Heat avocado oil in a heavy pot over medium-high heat. Sear venison in batches, about 3–4 minutes, until browned. Remove and set aside.
Add onion and celery to the pot, cooking 5–6 minutes until softened. Add garlic and cook 1 minute more.
Stir in broth, tomato paste, bay leaves, and thyme.
Return venison to the pot, cover, and simmer 1 hour 30 minutes to 2 hours, until tender.
Remove bay leaves, season with salt and pepper, and serve hot.