Reduce the heat to medium-low. Add another tablespoon of the oil and the onion to the pan, and cook, stirring occasionally, until the onion is softened. Add the coarsely chopped broccoli (not the florets), potato and chicken broth. Bring the broth to a boil, then reduce the heat and simmer, partially covered, for 20 minutes, stirring every so often, or until the broccoli and potatoes are very tender.
Meanwhile, on a rimmed baking sheet toss the florets with the remaining 2 teaspoons oil. Season with salt and pepper, then spread in an even layer. Roast in the top third of the oven for 5 minutes, or until lightly caramelized.
When the vegetables in the soup are tender, transfer the soup to a blender and puree, in batches, until smooth. Be careful and only fill the blender a third full each time.
Return the soup to the saucepan, along with the roasted broccoli florets and the Canadian bacon. Add the lemon juice, then season with salt and pepper. Add water, if necessary, to achieve the desired texture. Ladle the soup into 4 shallow soup bowls and top each portion with some of the cheddar.