Shred the cheese and measure out the sour cream and half and half, letting them all sit at room temperature.

Cook and crumble the ground beef over medium-high heat until it's cooked through, then drain the grease and set the beef aside.

While the beef cooks, peel and cut the potatoes, then boil them gently in salted water for 10-15 minutes until very fork tender. Drain the potatoes, gently mash them, and then stir in the sour cream and 1 tablespoon of butter.

Melt 2 tablespoons of butter over medium heat, add the diced onions and cook until softened (about 5 minutes), then add minced garlic and cook for 1 more minute.

Whisk in the flour and stir continuously with a silicone spatula for 1 full minute to remove any raw flour taste.

Gradually add the chicken broth in splashes, stirring continuously with a silicone spatula to loosen any beef remnants from the bottom of the pot for added flavor.

Stir in the Worcestershire sauce, Italian seasoning, mustard powder, and sage, then slowly add the half and half; bring to a boil and then reduce to a simmer.

Stir the mashed potatoes into the broth until well-combined, then use an immersion blender or transfer to a regular blender in batches to blend until creamy.

Add the cooked ground beef and frozen mixed vegetables to the soup and allow them to heat through for approximately 5 minutes.

Remove the soup from the heat and gradually sprinkle in the shredded cheddar cheese, stirring until it is completely combined and melted smoothly.

Taste the soup and season with additional salt and pepper if desired, then serve warm; note that the soup will continue to thicken as it sits.