Melt butter in a large dutch oven over medium heat. Once melted, saute shallots and garlic until soft and fragrant, about 2 minutes.
Add flour and all seasonings, stirring well. Allow seasonings to toast for 2-3 minutes.
Add potatoes, carrots and vegetable stock. Stir well being sure to scrape the browned bits from the bottom of the pot. Let simmer for 5 minutes, stirring frequently.
Stir in cream, bring to a boil, then reduce heat to medium-low and simmer for 20 minutesor until the potatoes and carrots are soft.
Remove from heat then stir in cheese until melted. Either pour into a blender and blend in batches or use an immersion hand blender directly in the dutch oven itself, blending until smooth.
Serve topped with sour cream and green onions if desired and enjoy!