Split the vanilla bean down the middle with a sharp knife and scrape out the seeds. Set aside pods and seeds.
Combine the milk and the cream in a large heavy bottomed saucepan and bring just to a boil. Turn off the heat, add the vanilla bean pods and the seeds, then cover and let steep for 30 minutes.
Whisk together the sugar, brown sugar and egg yolks until well mixed, will be light a fluffy.
Remove the cover from the saucepan and return the milk mixture just to a boil. Turn off the heat and slowly drizzle about 1/4 of the milk mixture into the egg yolk mixture, whisking continuously. Adding the milk mixture in a very slow drizzle will temper the eggs, slowly bringing them to a warmer temperature without cooking them. You can increase the drizzle to a little faster flow, still continuously whisking until all the milk mixture has been combined with the egg yolk mixture.
Pour the egg and milk mixture back into the saucepan and heat the mixture over medium heat, stirring continuously with a wooden spoon, be sure to scrape the bottom and corners of the pan as your stir. Continue cooking until mixture thickens into a custard and coats the back of the spoon. A good test is to run your finger down in a line across the back of the spoon. If the line fills in, it's not thickened enough yet. This can take anywhere from 2 to 10 minutes depending on the heat of your stove.
When custard is ready, pour it through a sieve into a metal or glass bowl. Remove the pods from the strainer and set aside (to make vanilla sugar!*). Use a rubber spatula to ensure that you scrape out all the vanilla bean seeds from the saucepan. Stir in vanilla extract.
Place bowl of custard into a larger bowl of ice water to help it cool, stirring the custard occasionally. Cover the surface of the custard with plastic wrap and chill in the refrigerator for a couple of hours. Once chilled, churn the chilled custard in your ice cream maker according to the manufacturer's instructions. Remove ice cream to a covered container and freeze until set.
*For the reserved pods, allow them to dry, then push down into a bowl or jar of white sugar and cover. Makes a lovely vanilla sugar!