Heat the oil over medium heat in a large pot or Dutch oven. Add the onion, celery, and carrots, sautéing for 3-4 minutes until the onion is translucent. This initial step is crucial for building a flavor base, as the gentle cooking of aromatics releases their natural sugars, enhancing the overall taste of the soup.

Add the garlic and sauté another minute. Be careful not to burn the garlic, as it can turn bitter quickly. This brief cooking time is enough to infuse the oil with its fragrant essence.

Stir in the potatoes, broth, salt, and pepper. Bring the mixture to a simmer, cover, and let it cook for 15 minutes, or until the potatoes are fork-tender. The simmering allows the potatoes to absorb the flavors, melding them into a cohesive, delicious whole.

Remove from heat, stir in the milk and cream, then add the cottage cheese. Blend with an immersion blender until smooth, or carefully blend in batches using a high-speed blender. Blending transforms the soup into a velvety, luscious texture that is both pleasing to the eye and palate.

Return the soup to the pot over low heat, stirring in the cheddar cheese until fully melted and the soup is smooth. Serve with chives and/or bacon crumbles. The addition of cheddar cheese not only enhances the flavor but also adds a beautiful, rich color to the soup.