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Heat the olive oil in the bottom of a Dutch oven or large stockpot for a minute over medium/high heat. Add the bacon to the pot and cook for about 7-10 minutes until crispy. Use a slotted spoon to remove the bacon and place it off to the side on a plate lined with a paper towel.
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Turn the heat down to low. Mix in the horseradish. Add the flour to the pot and whisk to combine with the bacon fat to make a roux. Slowly pour in the milk, whisking to combine the milk with the roux. Increase the heat to medium/low and bring to a simmer.
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Add potatoes to the pot, cover with lid, and let simmer for about 20 minutes until the potatoes are fork tender. Stir occasionally while simmering.
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Once the potatoes are tender, stir in the sour cream. Once it melts into the soup, add two of the chopped green onions, and salt and pepper to taste. Stir to combine.
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Remove from heat, allow to slightly cool before serving. If you want a thinner soup at this point add either more milk or a little chicken stock to thin it out.
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Top each bowl of soup with a heap of cheddar, some bacon, and some chopped green onions.
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To reheat the soup, add a little milk or chicken stock to make sure it doesn’t get too thick or clumpy.