In a large skillet over medium heat, add olive oil and heat for about 1 minute. Then add ground beef and onions; cook for 5-7 minutes until browned, breaking it apart. Drain excess grease.

Stir in minced garlic and cook for an additional minute until fragrant. Transfer mixture to slow cooker.

In the slow cooker, add potatoes, diced tomatoes, celery, and bell pepper. Pour in beef broth, dry mustard, and relish; stir to combine.

Season with salt and pepper; cover and cook on HIGH for 3-4 hours or LOW for 6-8 hours until vegetables are tender and soup thickens.

Check consistency; if too thick, stir in additional broth or water to reach desired texture.

Ladle soup into bowls and serve hot with crusty bread or a side salad.