Velvety Vermont cheddar soup made with sharp aged cheddar is a rich, vegetarian comfort food from the Green Mountain State. This family-friendly soup pairs beautifully with crusty bread on cold New England evenings.
In a heavy-bottomed Dutch oven, melt the unsalted butter over medium heat until foamy but not browned.
Add the chopped onion, celery, and carrot. Sauté for 6–8 minutes, stirring occasionally, until the vegetables are softened and lightly golden.
Stir in the diced potato and the all-purpose flour, cooking on medium-low heat while stirring constantly for 2 minutes to form a smooth roux and remove raw flour taste.
Gradually pour in the whole milk and vegetable broth, stirring or whisking constantly to prevent lumping. Raise heat to medium and bring the mixture almost to a simmer, then reduce heat to low.
Cover and cook gently for 15–18 minutes, stirring every few minutes, until potatoes are tender and soup base is thickened and creamy.
Stir in the Dijon mustard, Worcestershire sauce, salt, pepper, and smoked paprika. Remove from heat.
Add the shredded Vermont cheddar cheese in handfuls, stirring gently after each addition on very low heat until fully melted and the soup is velvety smooth (do not allow to boil after adding cheese). Serve hot.