Melt butter or chicken fat in a heavy-bottomed pot over medium heat.

Add onion and leeks and cook until softened, about 5-7 minutes.

Sprinkle in flour and stir well to combine.

Cook the flour mixture for 3-4 minutes, stirring constantly.

Whisk in chicken broth and white wine until smooth to avoid lumps.

Add carrots to the pot.

Bring the soup to a boil, then reduce heat and simmer for 15-20 minutes, or until the soup has thickened and carrots are tender.

Remove the pot from the heat.

Stir in grated cheddar cheese until melted and smooth.

Add Worcestershire sauce, cayenne pepper, and salt to taste.

Stir in heavy cream.

Heat gently until just hot, being careful not to boil.

Serve hot, garnished with chopped chives.