Melt butter, sweat onions and peppers (cover and cook slowly) until translucent, add chopped garlic. Sprinkle and stir in flour, cooking slowly for 15 minutes, stirring regularly. Add beer and whisk in until smooth. Melt in cream cheese. Add milk and bring slowly up to a simmer.
Add shredded cheese slowly. Stir in parsley and season to taste salt and pepper.