Add cubed potatoes to stock pot. Cover with chicken broth. The broth should just cover the potatoes. Add a little water if needed to cover potatoes. Toss in the Knorr bouillon cube. Heat over medium/high heat and bring to a boil. Then adjust heat to medium/low to continue cooking until potatoes are fork tender.
Meanwhile, in medium skillet, add butter, carrots, celery, and onion. Season with salt and pepper. The salt will help sweat the vegetables rather than brown them. That's what we want here, soft veggies. Cook over medium heat until vegetables are very soft, stirring occasionally. Once cooked thoroughly, remove skillet from heat to cool slightly while potatoes finish cooking.
When potatoes are fork tender, DO NOT DRAIN! Turn heat to low. Use potato masher to coarsely break up potatoes to desired size. I like it rather rustic, mostly smooth with some uneven sized chunks.
Meanwhile, add cooked carrots, celery, and onion to blender. Puree vegetables until smooth.
Add pureed vegetables to potato mixture. Stir to blend. Turn off heat.
Stir in milk, half & half, or cream. Add shredded cheese and stir to melt.
Garnish and serve. Enjoy!