Optional - Cold smoke the block of cheddar for about 1½-2 hours. After smoking, wrap the cheese block tightly in plastic wrap and refrigerate while the other ingredients are cooking. You can also smoke the cheese 1-2 days before, wrap in plastic wrap, and refrigerate until ready to use.
Optional - Place the bacon on a wire rack on top of a sheet tray. Smoke on the grill at 225℉ for about 2-2½ hours. Then remove from the grill, allow to cool slightly, and chop into small pieces. Reserve the bacon grease on the sheet tray. *Alternatively, you can chop the bacon slices and cook in a large skillet until crispy, reserving the grease.
Wash, peel, and cut the potatoes into cubes that are about ½" square. Soak the potatoes in a large bowl of cold water for about 5-10 minutes to remove excess starch, then drain.
Add the drained potatoes to a large pot with the chicken broth. Boil the potatoes in the broth until tender, about 15-20 minutes depending on the number of potatoes.
While the potatoes are cooking, cook the chopped smoked bacon in a skillet over medium heat, rendering out the fat until crispy. Remove some of the chopped bacon to save for garnish/serving.
Add the diced onions and jalapeno to the skillet with the remaining bacon and bacon grease. Sauté the vegetables until tender. When vegetables are almost done cooking, add the minced garlic and cook for about 2 minutes.
Add the flour to the skillet with the grease, bacon, and vegetables. Stir the flour in with the bacon grease to form a roux, and cook for about 3 minutes. *If needed, add about 1-2 tablespoons of butter to the bacon grease. Set the bacon and vegetable mixture to the side until ready to add to the soup.
When the potatoes are tender, transfer about 2 cups of the potatoes to a separate bowl. Use a large fork or masher to mash the boiled potatoes to a mashed potato-like consistency. Then add the mashed up potatoes back to the pot with the diced potatoes and chicken broth. This will act as a thickener for the baked potato soup.
Add the bacon and vegetable mixture to the pot with the potatoes. Then, stir in heavy cream or half and half. Fold in about ¾ of the shredded smoked cheddar cheese, reserving some for garnish. Mix well and allow to simmer for a few minutes.
Season the soup with salt, pepper, paprika, parsley, and cayenne pepper. Mix well. Stir in the sour cream.
Serve the potato soup with a dollop of sour cream, some crispy chopped bacon, more freshly grated sharp cheddar, and a sprinkle of green onions.