In a large bowl, whisk together egg yolks. Add granulated and brown sugars and whisk together until lightened in color and smooth.
Pour the half and half, the heavy cream, and the vanilla beans into a medium saucepan, over medium heat. Bring the mixture just to a simmer, stirring occasionally while pressing onto the vanilla beans to extract the flavor and the seeds. Once the cream has been gently scalded, remove the pot from the heat.
Use a ladle to transfer one spoonful at a time of the hot cream to the egg yolk mixture while whisking the entire time. Your goal is to slowly mix in the hot mixture to temper the eggs but not to cook them. Continue to slowly add the hot cream while whisking until all of it has been thoroughly combined.
Return the entire mixture to the saucepan and place over medium low heat. Continue to cook, stirring frequently, until the mixture thickens slightly and coats the back of a spoon. For me, this was more of a gut feel thing to know when it was ready, but you can definitely tell when the mixture has thickened. Do not let it get to the point where the eggs begin to cook. You should be able to touch the mixture with your finger without burning it.
Pour the mixture into a bowl and allow to sit at room temperature for 30 minutes.
Cover the bowl and refrigerate for at least four hours. You can also place the bowl inside a larger bowl that has ice in it for more rapid cooling.
Remove vanilla bean pods from the mixture, scraping out as many seeds as you can to stir back in. Pour ice cream base into an ice cream maker where the ice cream maker bowl has been frozen and process according to the manufacturer's directions. I was able to process the entire batch at once in my Cuisinart Ice Cream Maker. This should take approximately 25 to 35 minutes. Freeze for a couple of hours to allow the ice cream to harden. Then scoop and enjoy.