For the custard base and vanilla ice cream layer: In a medium saucepan over medium-low heat, combine the half-and-half and sugar. Stir it around to combine.
Using a small paring knife, split the vanilla bean down the middle. Scrape out the caviar inside and add it to the pan along with the bean. Stir the mixture around and heat it up until it's hot but not boiling.
Add the egg yolks to a medium bowl and whisk them vigorously until the yolks are slightly lighter in color, about 2 minutes.
Remove the vanilla bean from the saucepan. Grab a ladle of the hot half-and-half mixture and drizzle it very slowly into the yolks, whisking constantly. This will temper the egg yolks so that they don't scramble when they're added to the saucepan. Add another ladle of the hot liquid, and when it's mixed in, pour the egg mixture slowly into the half-and-half mixture, stirring with a spoon until the mixture is thick and coating the spoon, 2 minutes or so.
Set a fine-mesh strainer over a clean glass bowl and strain the custard. Don't worry if it looks a little lumpy! That just means you're perfectly imperfect. Add the heavy cream to the bowl and stir to combine. Divide the mixture into three pitchers; set aside one pitcher to work with for the chocolate ice cream layer, and chill the other two.
For the chocolate ice cream layer: Melt the dark chocolate chips with the heavy cream over a double boiler. When the chocolate and cream mixture is smooth and melted, add 1 cup of the reserved custard and combine. Return this mixture back to the pitcher. (This step is to ease the mixing process to make it easier to pour back into the custard and could therefore be omitted.) Whisk the cocoa into the pitcher. Pour into an ice cream maker and churn as per the manufacturer's instructions. (This will take approximately 1 hour.)
Line two 6-cup loaf pans with plastic wrap. Scoop half of the chocolate ice cream into each. Smooth them over and place in the freezer for at least 1 hour.
To make the vanilla ice-cream layer, add the second pitcher of custard to the ice cream maker and churn according to the instructions. (Again, approximately 1 hour.)
Remove the loaf pans from the freezer and spread half of the vanilla ice cream in each. Smooth and return to the freezer for at least 1 hour.
For the strawberry ice cream layer: Combine the strawberries, sugar and red food coloring in a blender and puree until smooth (or you can stop just short of smooth if you want a little texture). Pour the pureed strawberries into the final third of the chilled custard mixtures and stir. Pour into the ice cream maker and churn.
Remove the two pans from the freezer and scoop half of the strawberry ice cream into each, making the final layer. Smooth and return to the freezer for at least an hour.
To serve: Remove the loaf pans from the freezer, turn them upside down onto a serving plate and remove the plastic wrap. Slice neatly with a knife that has been dipped in very hot water.