Heat the Milk and Cream. In a medium saucepan, combine the milk, cream, 1/2 cup of sugar, and the vanilla beans (split and seeds scraped out) over medium heat. Heat until warm and steaming, about 170°F (77°C). Do not let it boil.
Beat the Egg Yolks. While the milk mixture is heating, beat the egg yolks and remaining 1/4 cup of sugar in a mixing bowl until light yellow and well combined.
Temper the Eggs. Gradually add half of the warm milk mixture to the egg yolks, whisking constantly to temper the eggs. Then pour the egg mixture back into the saucepan with the remaining milk and cream.
Cook the Custard. Cook the mixture over medium heat, stirring constantly, until it reaches 185°F (85°C) and thickens enough to coat the back of a spoon. Be careful not to boil the mixture. Remove from heat and stir in the pinch of salt and vanilla extract.
Strain and Chill. Strain the custard through a fine-mesh sieve into a clean bowl to remove the vanilla bean pods (if using) and any cooked egg bits. Cover and refrigerate for at least 4 hours, or overnight, until completely chilled.
Cook the Sugar for the Salted Caramel. In a medium saucepan, heat the sugar over medium heat, stirring constantly, until it melts into a deep amber-colored liquid. Be careful not to burn the sugar. It is going to melt, not dissolve. Once it's liquid, it will be very hot, so be careful!
Add Butter. Once the sugar is fully melted, carefully add the butter, whisking until fully combined.
Add Cream and Salt. Slowly drizzle in the heavy cream while whisking continuously (the mixture will bubble up). Continue to cook for another minute, then remove from heat and stir in the sea salt. Let the caramel cool to room temperature.
Freeze the Custard. Pour the chilled vanilla custard into your ice cream maker and churn according to the manufacturer’s instructions.
Swirl in the Caramel. When the ice cream reaches the consistency of soft serve, gently fold in the salted caramel, creating swirls without fully mixing it in.
Freeze. Transfer the ice cream to a loaf pan, cover with plastic wrap, and freeze for at least 4 hours or until firm. The ice cream will keep well, covered in the freezer, for up to one week.