Make an ice bath by filling a large bowl about a third full with ice cubes and adding a cup or so of water so they’re floating. Nest a smaller metal bowl (at least 2 quart) over the ice, pour 1 cup of the milk into the inner bowl, and rest a mesh strainer on top of it.
Spread 1½ cups sugar in the saucepan in an even layer. Cook over medium heat until caramelized, using the same method described in making the caramel praline.
Once caramelized, remove from heat and stir in the butter and salt, until butter is melted, then gradually whisk in the cream, stirring as you go. The caramel may harden and seize, but return it to the heat and continue to stir over low heat until any hard caramel is melted. Stir in the remaining 1 cup of the milk.
Whisk the yolks in a small bowl and gradually pour some of the warm caramel mixture over the yolks, whisking constantly. Scrape the warmed yolks back into the saucepan and cook the custard using a heatproof utensil, stirring constantly (scraping the bottom until the mixture thickens). If using an instant-read thermometer, it should read 160-170 F.
Pour the custard through the strainer into the milk set over the ice bath, add the vanilla, then stir frequently until the mixture is cooled down. Refrigerate at least 8 hours or until thoroughly chilled.
Freeze the mixture in your ice cream maker according to the manufacturer’s instructions.
While the ice cream is churning, crumble the hardened caramel praline into very little bits, about the size of very large confetti (about ½-inch).
Once your caramel ice cream is churned, quickly stir in the crushed caramel, then chill in the freezer until firm.