Season cube steaks generously with salt and pepper on both sides.
Heat vegetable oil in a large skillet or Dutch oven over medium-high heat until shimmering.
Add the cube steaks and sear for 2-3 minutes per side until nicely browned. Work in batches if necessary to avoid overcrowding.
Remove steaks and set aside on a plate.
In the same pan, add sliced onions and cook until softened and starting to brown, about 3-4 minutes.
Add minced garlic and cook for 30 seconds until fragrant.
Pour in beef broth and Worcestershire sauce, scraping the bottom of the pan to release any browned bits.
Add dried thyme and stir to combine.
Return the cube steaks to the pan, along with any accumulated juices.
Reduce heat to low, cover, and simmer for 1.5-2 hours until the steaks are fork-tender.
Remove steaks to a serving platter and keep warm.
In a small bowl, whisk together flour and cold water until smooth.
Increase heat to medium and slowly whisk the flour mixture into the pan juices.
Continue cooking, stirring constantly, until gravy thickens, about 2-3 minutes.
Pour gravy over cube steaks or serve on the side.