Pat lamb dry; season with salt and pepper. Melt 1 Tbsp. butter in a large skillet over medium-high heat. Working in batches, brown lamb on all sides, 5 minutes per batch. Transfer to a slow cooker.
Add onion to skillet and cook, stirring, until lightly browned, 3 minutes. Add broth and tomatoes. Increase heat to high and bring to a boil, stirring to pick up any browned bits in skillet. Pour tomato mixture over lamb in slow cooker. Cover; cook on low for 6 hours, until lamb is tender.
Strain stew; set aside meat and liquid. (You should have about 2 cups liquid.) In a bowl, using a fork, mix 1 Tbsp. butter with flour into a crumbly paste.
Bring stew liquid to a boil in a large saucepan over high heat. Whisking constantly, stir a few pieces of flour mixture into liquid. Continue until mixture is used up and liquid has thickened.
Reduce heat to medium; stir in lamb and vegetables. Cook until warmed through, 10 minutes. Season with salt and pepper. Serve hot.