Chop onions, carrots, celery and potatoes into small bite-size pieces.
Heat a stockpot to medium-high heat and add the onions, carrots, and celery. Stir and cook for 2 minutes or so, then add the diced potatoes. Cook for 5 minutes, seasoning with salt, pepper.
Pour in the broth and bring it to a gentle boil. Cook for 10 minutes, or until the potatoes are starting to get tender. Whisk together the flour and the milk, then pour into the soup and allow the soup to cook for another 5 minutes.
Remove half to 2/3 the soup and blend in a blender/food process until completely smooth. Pour it back into the soup pot and stir to combine.