1. Sprinkle beef with salt and pepper. Heat a large non stick skillet over medium-high heat. Add the beef and cook, turning occasionally, until browned, about 6 minutes.
2. Transfer the beef to a 5-6 quart slow cooker. Add the onions to the skillet; reduce the heat to medium. Cook, stirring occasionally, until the onions are lightly browned, about 8 minutes. Add the broth; bring to a boil, stirring constantly to scrape the brown bits from the bottom of the skillet. Transfer the onion mixture to the slow cooker. Add the potatoes, garlic, vinegar, brown sugar, mustard, thyme, and bay leaves. Pour 1/3 cup of the beer into a small bowl and refrigerate. Pour the remaining beer over the beef and vegetables. Press the potatoes into the liquid to cover. Top with an even layer of the carrots. Cover and cook until the beef and vegetables are fork-tender, 4-5 hours on high or low 8-10 hours on low.
3. About 20 minutes before the cooking time is up, whisk the flour and reserved 1/3 cup of beer until smooth. Stir in about 1/4 hot liquid from the slow cooker until blended. Stir the flour mixture into the slow cooker. Cover and cook on high until the mixture simmers and thickens, about 15 minutes. Discard the bay leaves.