Heat olive oil in a large soup pot over medium heat.
Add sliced sausage and cook until browned, then remove and set aside.
Add chopped onion to the pot and sauté until softened.
Stir in minced garlic and cook until fragrant.
Add diced potatoes, chicken broth, and beer to the pot.
Bring to a boil, then reduce heat and simmer for 20 minutes until potatoes are tender.
Lower heat and stir in heavy cream.
Gradually add shredded cheddar cheese, stirring until melted and smooth.
Add cooked sausage back to the pot.
Season with paprika, black pepper, and salt.
Simmer for 5 more minutes, then remove from heat.
Garnish with green onions and serve warm.