1. Preheat oven to 425°F (204°C).
2. Toss diced rutabagas and parsnips with olive oil, salt, and pepper. Spread on a lined baking sheet and roast until browned and cooked through, about 45 minutes to 1 hour.

For the Soup

1. Melt 4 tablespoons (1/2 stick) butter in a large stockpot over medium heat.
2. Add onions, garlic, and bay leaves; cook until onions are soft and translucent, about 20-30 minutes.
3. Remove onions with a slotted spoon and set aside.
4. Gently heat milk in a small saucepan over medium-low heat.
5. Add remaining butter to the stockpot and melt over low heat.
6. Add flour and cook, whisking constantly, until light golden brown, about 5 minutes.
7. Slowly whisk in hot milk until thickened.
8. Add cheese and stir until melted.
9. Add beer, vegetable stock, and adobo sauce; simmer gently.
10. Add onions and roasted vegetables; season with salt and pepper.
11. Cook over low heat for 30-40 minutes until thick.
12. Taste and adjust seasoning as needed.
13. Garnish with fresh parsley and serve with crusty bread.