Brown the Beef
Crumble the ground beef into a large stockpot over medium-high heat. Cook, stirring frequently, until evenly browned and no longer pink, about 7–10 minutes. Drain and discard excess grease.
Cook the Vegetables
Add the carrots, celery, and onion to the pot. Cook, stirring occasionally, until the vegetables begin to soften, about 5 minutes.
Add Remaining Ingredients
Stir in the potatoes, corn, green beans, undrained peas, tomato sauce, and crushed tomatoes. Season with black pepper, then add the bay leaf and thyme.
Simmer
Add up to ¼ cup water if needed to prevent sticking, adding more during cooking if the soup becomes too thick.
Cook Until Tender
Bring the soup to a gentle simmer. Cover and cook, stirring occasionally, until the potatoes are tender, about 1 hour.
Serve
Remove bay leaf before serving. Taste and adjust seasoning if needed.
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