In a medium saucepan, combine cream and milk. Heat over medium heat until it just begins to simmer. Remove from heat.
In another saucepan, combine sugar and water. Cook over medium-high heat, without stirring, until the mixture turns a deep amber color, about 8-10 minutes.
Slowly and carefully whisk the hot cream mixture into the caramel. The mixture will bubble up, so be cautious. Add salt and stir until smooth.
In a separate bowl, whisk egg yolks. Gradually whisk about 1 cup of the warm caramel cream into the yolks to temper them.
Pour the egg mixture back into the saucepan with the remaining caramel cream. Cook over medium heat, stirring constantly, until the mixture thickens and coats the back of a spoon.
Remove from heat and stir in vanilla extract. Strain the mixture through a fine-mesh sieve into a clean bowl.
Cover and refrigerate until completely chilled, at least 2 hours or overnight.
Pour the chilled mixture into your Cuisinart ice cream maker and churn according to the manufacturer's instructions, usually about 20-25 minutes.
In the last 5 minutes of churning, add the crushed pretzels.
Transfer the ice cream to a freezer-safe container and freeze for at least 4 hours before serving.