In a large, heavy pot over medium heat, cook the bacon slices until crisp, about 13-15 minutes. Remove them to a paper towel-lined plate, leaving some bacon fat in the pot for flavor (you can leave a tablespoon or two).

Add the butter to the pot and melt it over medium heat. Then add chopped onion, celery, and carrot. Cook until softened, about 6-8 minutes. Stir in minced garlic and thyme, cooking for another 30 seconds until fragrant.

Pour in the cubed Yukon Gold potatoes and chicken broth, ensuring the potatoes are covered (add a bit more broth or water if necessary). Bring to a simmer and cook until potatoes are tender, about 18-20 minutes.

For a smoother texture, you can partially blend the soup using an immersion blender or by transferring half to a blender, then return it. Leave some chunks for bite. I usually skip this step.

Lower the heat and stir in the heavy cream. Gradually mix in the freshly grated cheddar until melted and smooth. Season with salt and pepper to taste.

Crumble the cooked bacon on top (reserve a few pieces for garnish), drizzle a little extra cream if desired, and sprinkle more cheddar.