The classic brandy cocktail would be the Sidecar. 2 parts brandy to 1 part Cointreau and 1 part lemon juice. Shake and double strain into a coupe.

That said, it sounds like you really want to feature the cognac, not bury it. Maybe consider something like a Vieux Carre or a Brandy Crusta.

The Vieux Carre is, in my opinion, one of the finest cocktails ever devised. It's like an elevated Manhattan. It's so good that after you try one you'll never want a Manhattan again.

You do 1oz each of bourbon, brandy, and sweet vermouth. Add 2 dashes each of Angostura and Peychauds bitters, stir over ice and pour into a coup. Traditionally, you'd float a barspoon of Benedictine on top, but you could also do a rinse with it (wash a splash around the inside of the glass and then toss out). If you're avoiding American, you'll want a good Canadian whisky, something like an Alberta Premium Select if you can get it, not too heavy on the rye spice if you want to emphasize the cognac. Garnish varies, I've seen lemon and orange swathes, but I'm partial to a luxardo cherry.