Chop the onion, celery, and garlic. Then peel the potatoes and cut them into 3/4 inch chunks. Place the potato chunks in a bowl of cold water so they don't brown.: The kitchen should smell faintly sweet from the raw onion and sharp from the minced garlic , and you will notice the bright pale flesh of the potatoes shining as you cut. Cold water prevents oxidation, keeping the cut surfaces from turning gray while you work. Use a firm knife and steady board to make even 3/4 inch cubes so they cook uniformly. Rinse the potato pieces briefly to remove excess starch, and keep them submerged until you're ready to add them to the pot. A common mistake is cutting uneven pieces, which leads to some chunks disintegrating while others remain undercooked.
Place a large 7-8 quart pot over medium heat. Add the butter. Once melted, add the onions, celery and minced garlic. Sauté for 3-5 minutes to soften, stirring each minute.: As the butter melts, it will foam slightly and release a rich, creamy scent. Add the chopped onion and celery and you should hear a gentle, steady sizzle, not a frantic crackle. Stirring every minute encourages even softening and prevents hot spots. After a few minutes the onion will become translucent and faintly sweet, while the celery will soften but retain some texture. Add the minced garlic toward the end of this window so it warms through without burning, which would turn it bitter. If the pan browns too quickly, lower the heat; burning the aromatics is the most common misstep here.
Drain off the water and add the potatoes to the pot. Add 8 cups fresh water, chicken base, and rosemary. Cover and simmer for 30 minutes, until the potatoes are fork-tender.: When you add the drained potatoes , they will hiss briefly as they meet the warm pot. Pour in the 8 cups of fresh water so the potatoes are submerged, then stir in the concentrated chicken base and sprinkle the rosemary . Bring the liquid to a gentle simmer with the lid on, then lower the heat to maintain a steady, small bubble. During simmering, watch the surface for occasional gentle movement and aroma rising from the pot; the scent will deepen into savory, herbaceous notes. Check tenderness by piercing a large chunk with a fork; it should slide in with little resistance. If they are still firm, continue simmering in five minute increments. Avoid boiling violently, which can break the chunks apart unevenly.
Use a potato masher to gently mash approximately 1/3 of the potatoes. You want the soup base to be thick, but to still see plenty of chunks.: With the pot off or on very low heat, press down on a third of the potatoes until they collapse and thicken the broth. The aroma will become fuller and the surface slightly velvety as starch releases. Leaving most chunks intact preserves bite, while the mashed portion creates body and creaminess without dairy heavy techniques. Work gently and avoid over-mashing which would make the soup gummy. If you accidentally mash too much, loosen with a little reserved hot water to regain the right balance.
Stir in the sour cream, grated parmesan cheese, and parsley. Taste, then salt and pepper as needed. Simmer another 5 minutes to thicken. Serve warm with an extra sprinkle of parmesan and parsley.: When you fold in the sour cream and grated parmesan cheese , the broth should take on a richer sheen and a slightly tangy warmth. The parsley will flash a brighter aroma, and the whole pot will smell layered and rounded. Taste before adding salt and pepper , because the chicken base and parmesan cheese already contribute sodium. Let the soup simmer gently for about five minutes so flavors marry and the texture thickens slightly. Serve warm, noticing the creamy mouthfeel and scattered chunks, and garnish with a little extra parmesan cheese and parsley for visual contrast. A frequent mistake is overheating after adding dairy, which can break the texture, so keep the heat low.