Prepare the venison backstrap by trimming away any silverskin or fat. Pat dry with paper towels and season generously with salt and pepper on all sides.
Heat olive oil in a large skillet over medium-high heat. Once hot, sear the venison pieces on all sides until nicely browned, about 2 minutes per side.
Place sliced onion rings in the bottom of your slow cooker, creating a bed for the meat.
Arrange seared venison backstrap pieces on top of the onions.
In a mixing bowl, combine beef broth, dry onion soup mix, dry cream of mushroom soup mix, minced garlic, Worcestershire sauce, dried thyme, and dried rosemary. Whisk until well combined.
Pour the liquid mixture over the venison in the slow cooker, ensuring meat is mostly covered.
Cover and cook on LOW for 6-7 hours or on HIGH for 3-4 hours. The venison is done when it's fork-tender but not falling apart.
Optional: 30 minutes before serving, mix cornstarch with cold water to create a slurry. Stir into the cooking liquid and continue cooking until gravy thickens.
Allow meat to rest in the warm cooking liquid for 10-15 minutes before serving.