GROUND BEEF: Heat a very large pot (I recommend cast iron), over high heat. Drizzle in 1 tbsp oil. Once oil is hot, add in the ground beef and season to taste (I add 1/2 tsp salt & 1/4 tsp pepper). Let beef sear for a minute per side then use a wooden spoon to crumble and cook until it is completely browned through. Use a slotted spoon to remove the beef to a separate bowl. Drain off any grease except for 1 tablespoon. If there is no grease, add 1 tablespoon olive oil to the pot.
VEGGIES: In the same pot with 1 tablespoon grease or olive oil, melt 1 tablespoon of the butter. Reduce heat to medium. Add the diced carrots, celery and onion. Season again (I add 1/2 tsp salt & 1/4 tsp pepper). Sauté 5-7 minutes or until tender (if not diced small, you may need 7-10 minutes). Add garlic, seasonings (1 tsp dried parsley, 1 tsp dried basil, 1/2 tsp ground mustard), and potatoes. Sauté, stirring constantly for 1 minute.
SIMMER: Add in chicken stock or broth and stir. Bring to a boil over high heat, then reduce heat to medium-low, cover with lid, and cook 15-20 minutes or until the potatoes are fork tender (easily pierced with a fork).
CREAM SAUCE: Meanwhile, melt remaining 4 tablespoons butter in a medium saucepan over medium heat. Stir in flour and cook, whisking constantly, for 1 minute. While whisking vigorously, slowly pour in milk, whisking well until smooth. Cook, stirring constantly, until mixture begins to gently boil and thicken (See Note 4). Once thickened, reduce heat to lowest setting and stir in the heavy cream and sour cream. Whisk until completely smooth.
FINISHING: Remove sauce from heat and once all soup veggies are tender, pour the milk/cream mixture into the soup and stir. Lower heat to lowest setting and return ground beef; mix through. Add in the shredded cheese. Mix gently until cheese is fully melted. Taste soup and season if needed with additional salt and pepper. Serve warm with freshly chopped parsley or thyme and bread!
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Notes
Note 1:Mirepoix: Use a food processor to quickly chop equal amounts of onion, carrot, and celery or you can buy this mix labeled "mirepoix" (already prepped onion, celery, carrots) at a lot of stores in the produce section or frozen vegetable section of the store.Note 2: Potatoes: Cut potatoes into 1/2-inch pieces. If using gold potatoes, no need to peel (the skin is so delicate). With other potatoes like russets, you may want to peel first.Note 3: Cheddar cheese: Use sharp or extra-sharp Cheddar (which indicates a more aged cheese that will deliver a richer and more pungent flavor). Grate the cheese fresh; already-grated packaged cheese will give the soup a powdery texture and won't melt as nicely. You can use a food processor to quickly grate cheese!Note 4: Thickness check: The sauce should be thick enough to coat the back of a wooden spoon. Lift up the spoon and immediately trace a line across the back of the spoon with your fingertip. If the line retains a clear track, the sauce is thick enough. If not, the sauce needs to be cooked a bit longer.