In a large, heavy-bottomed pot or Dutch oven, heat over medium heat. Add the ground beef and cook, breaking it apart with a spatula, until it's no longer pink and nicely browned. Drain any excess fat from the pot.
To the pot, add the finely diced onion and minced garlic. Sauté for about 2-3 minutes, or until the onions are soft and translucent, stirring occasionally to prevent burning.
Next, incorporate the diced potatoes, beef broth, shredded carrots, Worcestershire sauce, tomato paste, smoked paprika, salt, and pepper. Stir well to combine all the ingredients smoothly.
Increase the heat and bring the mixture to a rolling boil. Once boiling, reduce the heat to a low simmer and cover. Allow the soup to simmer for approximately 15-20 minutes, or until the potatoes are tender when pierced with a fork.
Stir in the heavy cream and shredded cheddar cheese gradually, mixing continuously until the cheese fully melts and the soup becomes thick and creamy.
If using, fold in the crumbled bacon and frozen peas, mixing well to distribute. Let the soup continue to heat through for an additional 5 minutes, stirring occasionally.
Before serving, taste the soup and adjust seasoning with more salt and pepper if necessary.
Notes
For a complete meal experience, serve with slices of crusty bread for dipping.