Heat 1 tablespoon oil in a large pot over high heat. Add the ground beef, season with 1/2 teaspoon each salt & pepper, and cook until browned and crumbled. Transfer the beef to a bowl.: The moment the large pot heats and the oil shimmers you will hear the first sizzle when the ground beef hits the pan, that sharp sear is what creates deep savory notes. Let the meat sit briefly before stirring so those brown crusty bits form, then break it up as it browns to develop even caramelization. You want a rich, browned color with small browned bits visible, not grey and steamed. If the pan becomes overloaded and the beef steams rather than browns, remove some liquid or brown in batches. A common mistake is stirring too often early on, which prevents proper browning, so allow contact time for flavor to build.
In the same pot, add remaining 1 tablespoon oil and 1 tablespoon butter over medium-high heat. Add the mirepoix, season with 3/4 teaspoon each salt and pepper, and sauté for 7-8 minutes, or until tender. Add garlic, parsley, basil, and mustard powder, and cook for 1 minute.: As the mirepoix hits the pan the vegetables will soften and release a sweet aroma, and you should see them turn translucent and slightly glossy. The butter adds a silky coating while the oil raises the smoke point for even cooking. When you add the minced garlic and dried herbs, the scent will become bright and herbaceous, but be careful to keep the heat moderate so the garlic does not brown and become bitter. If the vegetables start to brown too quickly, lower the heat and stir more frequently. A frequent error here is rushing the sauté; under cooked aromatics will leave the soup tasting one dimensional.
Pour in the chicken broth and bring to a boil. Add the pasta and cook 2 minutes less than the package directions (it will cook more!): When the chicken broth simmers you will smell a savory lift as the pan fond dissolves into the liquid, which deepens the soup base. Add the elbow macaroni and watch the pot return to a gentle boil, counting the time carefully. Because the pasta will finish cooking in the combined mixture, pulling it a hair under done ensures it keeps a pleasant bite rather than becoming mushy. Stir occasionally to prevent sticking, especially around the bottom. A typical slip is overcooking the pasta here, which makes the final texture limp, so set a timer and taste a piece before draining none needed, just leave it in the pot to finish.
In a separate medium pot, melt the remaining 4 tablespoons butter over medium heat. Add flour and whisk constantly for 1 minute. Slowly whisk in the milk and cook, stirring often, until nicely thickened (see note 3). Reduce the heat to low, then whisk in heavy cream and sour cream until smooth.: The roux begins with the sound of gentle bubbling as the melted butter and flour combine, and whisking transforms it into a pale paste that toasts slightly. When you add the milk gradually the mixture will go from chalky to silky, and you will notice the sauce thicken enough to coat the back of a spoon. Lowering the heat before adding the heavy cream and sour cream helps prevent scorching and separation, yielding a glossy, velvety sauce. If you rush and add cold milk too fast, lumps can form; to fix this, whisk vigorously and warm gently until smooth. A common mistake is overheating which can curdle dairy, so keep the heat moderate and patient stirring is your friend.
Pour the cream mixture and cooked beef back into the soup. Stir and cook until slightly thickened. Reduce heat to low and add cheese a handful at a time, stirring until melted. Taste and season with additional salt and pepper, if needed. Troubleshoot: If the soup is too thin, increase the heat slightly and simmer until it reaches your desired thickness. If it’s too thick, stir in a little broth to loosen it up.: If the soup is too thin, increase the heat slightly and simmer until it reaches your desired thickness. If it’s too thick, stir in a little broth to loosen it up. : As the two pots marry, you will notice the aroma combine into a richer, creamier scent and the surface will develop a silky sheen. Stirring gently helps the sauce incorporate with the broth and pasta, and adding the Cheddar cheese slowly allows it to melt into a smooth, glossy finish rather than clumping. Taste frequently for seasoning balance because cheeses and broths vary in saltiness. If the mixture begins to separate or look grainy, lower the heat and whisk steadily, adding a splash of warm broth if necessary. Many home cooks add all the cheese at once which can lead to clumps, so patience here makes for the best texture.
Ladle into bowls and serve warm with buttered toasted bread, if desired.: The final serving should steam gently, and you will see strings of melted Cheddar cheese and tender bits of ground beef interspersed with caramel colored pasta. A piece of buttered crusty bread provides a pleasing contrast, perfect for sopping up the creamy broth. Serve hot, and encourage stirring just before serving to redistribute any settled cheese. A common oversight is letting the soup sit too long without stirring which causes the pasta to absorb excess liquid and the texture to thicken undesirably, so serve promptly or store separately as needed.