Add 1 cup of sugar to a medium saucepan over medium heat.
Using a fork, stir the sugar constantly so it heats evenly.
Once it starts to melt, stop stirring and just swirl the pan occasionally so the sugar continues to melt evenly.
Cook until dark amber.
Add 1 ½ cups of the heavy cream. The mixture will boil but don't worry - just cook and stir until it becomes caramel. Remove from heat and cool for 20 minutes.
Bring the remaining 1 cup of cream, remaining ¼ cup sugar, milk, sea salt, and vanilla to a boil in a small saucepan.
In a separate bowl, whisk together the eggs. Add 1 cup of the hot milk/cream mixture to the eggs and whisk to combine, to temper the eggs.
Add this mixture back into the saucepan and continue to cook until the mixture thickens and reaches 170 degrees F.
Add this mixture to the caramel and stir to combine. Pour the ice cream mixture through a fine mesh sieve and then place in a covered bowl. Refrigerate for at least 3 hours.
Add the cold ice cream mixture to an ice cream maker and churn for 10-15 minutes.
It will be pretty soft. You can eat now like soft serve, or completely freeze in an airtight container.
Enjoy!