In a heavy-bottomed saucepan, combine granulated sugar and light corn syrup. Cook over medium heat, stirring gently, until the mixture turns a deep amber color, roughly 8 to 10 minutes. Remove from heat and whisk in unsalted butter until smooth. Allow it to cool slightly before swirling into the ice cream.

Heat heavy cream and whole milk in a saucepan over medium until barely simmering, about 5 minutes. Meanwhile, whisk egg yolks and remaining sugar in a bowl until pale and frothy. Gradually add the hot cream mixture to the yolks, whisking to prevent curdling. Return the mixture to the saucepan.

Stir the custard mixture constantly over low heat until it thickens enough to coat the back of the spoon, achieving about 170°F, roughly 5 to 7 minutes. Strain through a fine-mesh sieve to remove lumps and stir in vanilla extract. Let it cool completely.

Gently swirl the prepared salted caramel into the cooled custard. Pour into the Ninja Creami pint container, seal well, and freeze for at least 24 hours to firm up.

After freezing, remove the pint container and process on the 'Ice Cream' setting of the Ninja Creami for about a minute. Use 'Re-spin' for a smoother texture. Serve topped with flaky sea salt.