Thinly slice the green onions, separating the white and light green parts from the dark green tops.
Set the green tops aside for garnish.
In a large saucepan or Dutch oven, heat 2 tablespoons (30 ml / 1 fl oz) of olive oil over medium heat.
Add the white and light green parts of the onions and cook, stirring occasionally, until softened and fragrant, about 3-4 minutes.
Transfer the cooked onions to a blender.
Add 1 cup (240 ml) of the hash brown potatoes, the drained roasted red peppers, and the lager.
Cover and blend until the mixture is almost smooth.
Pour the blended mixture back into the saucepan, bring to a boil, then reduce the heat to a simmer.
Cook, uncovered, for 5 minutes to allow the flavors to meld.
Stir in the milk and shredded cheese.
Continue to cook and stir gently over medium heat until the cheese is completely melted and the soup is smooth and heated through. Be careful not to let the soup boil after adding the cheese.
While the soup is heating, prepare the topping.
In a small skillet, heat the remaining 1 tablespoon (15 ml / 0.5 fl oz) of olive oil over medium-high heat.
Add the remaining 1 cup (240 ml) of hash brown potatoes and cook, stirring occasionally, for about 8 minutes, or until they are golden brown and crispy.
Transfer the crispy potatoes to a paper towel-lined plate to drain any excess oil, then sprinkle with paprika.
Ladle the hot soup into four bowls.
Garnish generously with the crispy hash browns and the reserved sliced green onion tops.
Add an extra sprinkle of paprika, if desired, and serve immediately.
Add a pinch of cayenne pepper or a dash of your favorite hot sauce along with the paprika for a gentle kick of heat.
