Stir together stock, diced onion and broccoli in a medium saucepan. Heat over medium heat until it comes to a low boil. Reduce heat to medium and continue boiling for about 5 minutes, or until the onions are tender. Stir in the evaporated milk and continue cooking for 3 minutes or until the mixture returns to a simmer. Remove from heat and stir in the cheese until melted.

Season soup with salt and pepper to taste.

Serve warm.

**As I said above, some brands of shredded cheese melt more easily than others. To play it safe, I recommend buying a block of cheddar and shredding it yourself just before adding in the cheese. But I used Kraft brand for this recipe, and it melted perfectly!**