Heat 1 tbsp olive oil in a large pot over high heat. Add ground beef, season with 1/2 teaspoon each salt and pepper, and cook and crumble until browned through. Transfer to a bowl and drain the pot, leaving behind 1 tbsp grease. If no grease is left behind, add 1 tbsp olive oil.
In the same pot, melt 1 tbsp butter over medium-high heat. Add mirepoix, season with 1/2 teaspoon each salt and pepper, and sauté for 5-7 minutes until tender. Add garlic, parsley, basil, mustard powder, and potatoes; sauté for 1 minute.
Pour in chicken stock. Bring to a boil, then reduce to medium-low. Cover and cook for 15-20 minutes, until potatoes are tender.
In a separate pot, melt remaining 4 tbsp butter over medium heat. Add flour, whisking constantly for 1 minute. Slowly whisk in milk and cook, whisking constantly, until thickened (see note 5). Reduce heat to low, stir in heavy cream and sour cream, and whisk until smooth.
Add cream mixture and cooked beef back to the soup. Stir in shredded cheese a handful at a time until melted. Taste soup and season if needed with additional salt and pepper.
Optionally garnish with fresh parsley or thyme and serve with buttered toasted bread.
Video
Notes
Note 1: Use equal parts diced onion, carrot, and celery (3/4 cup each) or buy a mix labeled "mirepoix" in the produce section or frozen vegetable section of the store.Note 2: For gold potatoes, no need to peel. If using russets, peel first. Dice into 1/2-inch pieces.Note 3: Use freshly shredded sharp or extra sharp Cheddar for the best flavor and melt.Note 4: I love to use fresh parsley or thyme for garnish, and hearty toasted buttered bread is great for dipping!Note 5: Sauce Thickness Check: Coat the back of a wooden spoon in the sauce, then draw a line with your finger. If it holds, the sauce is ready.Storage: Store the soup in an airtight container in the fridge for 3-5 days. To reheat, warm on low and stir often, avoiding boiling; add milk or broth if needed to thin. For freezing, let the soup cool, transfer to an airtight bag, and freeze for up to 3 months. Thaw overnight in the fridge before reheating.