Heat the oil in a large skillet over medium-high heat. Add the cubed beef and brown it on all sides. Transfer the beef to a 5- to 6-quart slow cooker.
In the same skillet, add the chopped carrots, celery, and onion. Cook until the onion softens, stirring occasionally.
Stir in the tomato paste, minced garlic, salt, dried parsley, thyme, paprika, and pepper. Cook for 1 minute to allow the spices to become fragrant.
Transfer the sautéed vegetables from the skillet to the slow cooker with the browned beef. Mix everything together.
Pour in the low-sodium beef broth, chopped potatoes, diced tomatoes with juice, green beans, marinara sauce, corn, and add the bay leaf. Stir gently.
Cover the slow cooker and cook on low for 7 to 8 hours.
After cooking, remove the bay leaf and taste the soup. Adjust seasonings as desired.
Serve immediately or keep on warm until ready to enjoy, pairing it with crusty bread.