In a large bowl, combine the sugar, eggs and cornstarch and beat with a hand mixer until thick and pale yellow, about 3-5 minutes. Set aside.
In a medium saucepan, heat the half and half to just barely a simmer. In a slow steady stream, add the hot half and half to the egg mixture, beating constantly at a medium speed. When mixture is combined, pour it back into the pan and heat over medium heat, stirring constantly until mixture thickens.
Place a fine mesh sieve over a large bowl and pour the custard through the sieve to remove any large egg particles. Scrape the outside of the sieve to capture as much of the custard as possible. Cool for 10 minutes, then stir in the heavy cream and vanilla. Chill for at least 2 hours or overnight.
Follow the manufacturer's instructions for your churn. In the last few minutes before the frozen custard is ready, add the pretzel pieces and churn until fully combined.
Spoon about ¼ of the ice cream into a freezer-safe container. Drizzle several tablespoons of stout caramel over it. Continue layering in this fashion and finish with ice cream on top. Cover with plastic wrap and freeze for several hours or overnight.
Serve with extra pretzels and caramel sauce if desired.
Notes
You can make the stout caramel sauce up to a week ahead.
You can make the custard a day ahead, churn and assemble the next day.
Store in an airtight container in the freezer.
When stored in a proper airtight container, it will keep for 1-3 months.