Heat a large stockpot or Dutch oven over medium heat. Add the bacon and cook, stirring occasionally, until it is browned and crisp-- about 7 minutes.
Remove the bacon using a slotted spoon and place it on a paper towel to drain. Remove all but one tablespoon of bacon drippings from the pan.
Add the onion and cook, stirring occasionally until it is soft and translucent-- about 3 minutes. Stir in the garlic and rosemary and cook for an additional minute.
Add the butter and allow it to melt-- then sprinkle over the flour and stir until it begins to form a thick paste. Slowly add the chicken broth, stirring constantly. If there are any large lumps of flour, whisk the soup vigorously until they have dissolved.
Next, add the beer and heavy cream. Stir to combine. Allow the soup to simmer for 5 minutes so it can thicken slightly. Slowly add the cheese, stirring as you add. Keep stirring until all of the cheese has melted.
Serve the soup topped with the crispy bacon bites and sliced green onions with pretzels or sourdough on the side.
Store any leftover soup in an airtight container in the fridge for up to three days.