1. Make the Caramel Praline Mix-In: Line a baking sheet with parchment paper or a silicone baking mat.
2. Place the sugar in an even layer in a medium saucepan and place over medium heat until the edges begin to melt. Gently stir with a heatproof spatula from the bottom and edges towards the center until all the sugar is dissolved. Continue to cook, stirring occasionally, until the caramel begins to smoke and emits a nutty, almost-burnt smell, a couple of minutes. Remove from the heat.
3. Immediately sprinkle with the flaked salt (do not stir), then pour the caramel onto the prepared baking sheet, tilting and swirling it to form an extremely thin layer. Set aside to harden and cool.
4. Make the Ice Cream Custard: Fill a large bowl one-third full with ice cubes and add a cup of water. Nest a smaller metal bowl (at least 2 quarts) over the ice, pour 1 cup of the milk into the bowl, and rest a fine-mesh strainer on top.
5. Spread the sugar in a medium saucepan in an even layer. Cook over medium heat until caramelized, using the same method described in Step #2.
6. Once the sugar has caramelized, remove from heat and stir in the butter and salt, until butter is melted, then gradually whisk in the cream. If the caramel hardens, return it to the stove and stir over low heat until completely melted. Whisk in the remaining 1 cup of the milk.
7. In a small bowl, whisk the egg yolks, then gradually whisk in about ½ cup of the warm caramel mixture. Scrape the warmed yolks back into the saucepan and cook the custard over medium heat using a heatproof spatula, stirring and scraping the pan constantly until the mixture thickens and reads 170 to 175 degrees F on an instant-read thermometer.
8. Pour the custard through the strainer into the milk set over the ice bath, and stir in the vanilla. Stir occasionally, until the mixture is cool. Cover and transfer the custard to the refrigerator until completely chilled, at least 8 hours or overnight
9. 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 ½-inch pieces. Add the praline pieces during the last minute of churning. Transfer the ice cream to a freezer-safe container and freeze for at least 2 hours before serving.