salted caramel frozen custard

This recipe from an old issue of Gourmet, courtesy Epicurious.

INGREDIENTS:
1 1/4 cups sugar, divided
2 1/4 cups heavy cream, divided
1/2 teaspoon flaky sea salt
1/2 teaspoon pure vanilla extract
1 cup whole milk
3 large eggs

Heat 1 cup sugar in a dry 10-inch heavy skillet over medium heat, stirring with a fork to heat sugar evenly, until it starts to melt, then stop stirring and cook, swirling skillet occasionally so sugar melts evenly, until it is dark amber. 

Add 1 1/4 cups cream and cook, stirring, until all of caramel has dissolved. (Ed note: If this step is not scary, and your mixture doesn't bubble up into something monstrous and horrible, you've done it wrong. Go back and try again.) Transfer to a bowl and stir in sea salt and vanilla. Cool to room temperature. 

Meanwhile, bring milk, remaining cup cream, and remaining 1/4 cup sugar just to a boil in a small heavy saucepan, stirring occasionally. 

Lightly whisk eggs in a medium bowl, then add half of hot milk mixture in a slow stream, whisking constantly. Pour back into saucepan and cook over medium heat, stirring constantly with a wooden spoon, until custard coats back of spoon. DO NOT LET BOIL!

Pour custard through a fine-mesh sieve into a large bowl, then stir in cooled caramel. 

Chill custard, stirring occasionally, until very cold, 3 to 6 hours. 

Freeze custard in ice cream maker (it will still be quite soft), then transfer to an airtight container and put in freezer to firm up.

NOTES: The recipe really captures the caramel flavor, the texture too -- velvety -- the salt not so much. Next time try a different kind of salt maybe? Or more of it? And maybe add some on top, right at the end. Lots of salt options.

The other problem is... I don't quite know how to put it. Temperature? It didn't feel cold to the taste. Again, maybe it was the salt maybe the number of eggs, but it was cool, not cold.