Mix all the ingredients together in a large saucepan. Don't use copper or aluminum. They can give the wine a metallic taste.
Bring the mixture to just under a simmer over the lowest heat setting on the stovetop. No boiling!
When the sugar has dissolved and the wine is hot, strain the wine by pouring it through a fine-mesh sieve or a cheesecloth-lined colander. Add 1-2 teaspoons of Cognac to a pre-warmed mug and ladle the mulled wine over it.