In a medium saucepan, combine the milk, brown sugar, vanilla bean and seeds and salt. Cook over moderately low heat, stirring occasionally, until the milk is steaming, about 8 minutes; do not let it boil. Remove from the heat and keep warm. Discard the vanilla bean.
Meanwhile, in a bowl, whisk the egg yolks with the granulated sugar until thick and pale. Whisk in half of the warm milk, then whisk in the remaining milk. Return the mixture to the saucepan and cook, stirring frequently, until the custard thickens slightly and coats the back of a spoon, 8 to 10 minutes. Stir in the cream. Strain the custard into a bowl and chill thoroughly. Transfer to an ice cream maker and freeze according to the manufacturer's instructions.