1) Heat the cream, sugar, vanilla extract, and vanilla seeds in a small saucepan only until the sugar is dissolved. Be sure the sugar is dissolved - you will no longer feel any grittiness from the sugar if you rub some cream between your fingers.
2) Sieve into a bowl, cover, and chill very well. Add the Armagnac and freeze the mixture in an ice cream freezer according to the manufacturer's directions. Spoon into a freezer container and freezer for a few hours before serving.