Season the beef sirloin tips with salt and black pepper.
Heat olive oil in a large skillet over medium-high heat.
Add the beef tips in batches and brown on all sides, about 3-4 minutes per batch. Transfer browned beef to the slow cooker.
In the same skillet, add the chopped onion and cook until softened, about 3 minutes.
Add minced garlic and cook for an additional 30 seconds until fragrant.
Pour in the beef broth and red wine, scraping the bottom of the skillet to loosen browned bits.
Stir in Worcestershire sauce, dried thyme, and dried rosemary.
Pour the mixture over the beef tips in the slow cooker.
Cover and cook on low for 6 hours, or until the beef is tender.
About 30 minutes before serving, mix all-purpose flour with 2 tablespoons cold water to make a slurry.
Stir the slurry into the slow cooker to thicken the gravy.
If additional thickening is desired, mix cornstarch with 2 tablespoons cold water and stir into the slow cooker, cooking for another 10-15 minutes until gravy thickens.
Taste and adjust seasoning with salt and pepper as needed.
Serve the beef tips with gravy over mashed potatoes, rice, or egg noodles.