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In a large dutch oven or pot, melt the butter over medium heat.
Add the diced onion and cook until softened and translucent. Add the garlic and cook an additional 30 seconds.
Stir in the flour to make a thick paste. Allow this to cook for about 1-2 minutes, just to cook the flour.
Stir in the salt, pepper, and paprika. Pour in the chicken stock. Stir to combine.
Add the diced potatoes. Cook for about 10-15 minutes over medium heat.
Add in the corn and continue to cook for another 10 minutes, until corn is heated through and the potatoes are fork tender.
Turn off the heat and using an immersion blender blend up the soup to desired consistency. I prefer to leave some chunks of corn and potato in mine. The more you blend the thicker the soup will be. If you don't have an immersion blender, you can remove about half of the soup carefully and blend in a blender or food processor. Then return to the pot.
After soup is blended, add in the ham. I prefer giving my ham a quick sear in a separate pan over medium high heat for about 5 minutes before adding to the soup. This is completely optional. If you skip this step, turn the heat back on the soup and let the soup cook longer to make sure the ham is warmed through.
Add in the half and half. Stir to combine.
Serve soup warm with a garnish of fresh chives, or parsley and a dash of fresh ground pepper.