Place 1 cup of sugar in a heavy-bottomed kettle. Melt over medium-high heat. As the sugar begins to melt around the edges of the pan, slowly pull into the middle to ensure even melting.
1 ¼ cups granulated sugar
When the sugar has reached a deep amber color and is all melted, pull off the heat and slowly add 1 cup of milk. Stir constantly until the milk is fully incorporated. If the sugar hardens or clumps, set it back over medium heat to melt the mixture. When smooth, set the caramel aside.
2 cups + 2 tbsp whole milk
In a separate kettle, heat 1 cup milk, heavy cream, remaining ¼ cup sugar, corn syrup, and salt. Bring to a boil.
1 ¼ cups granulated sugar, 1 ¼ cups heavy cream, 2 tbsp light corn syrup, 1 tsp kosher salt
While the milk mixture is heating, in a separate bowl, whisk together the remaining 2 tablespoons milk and cornstarch until smooth. Once the milk mixture is boiling, allow to boil 2 minutes. Remove from heat and slowly whisk in the cornstarch slurry.
1 ½ tbsp cornstarch
Return to medium heat and whisk for 30 seconds until slightly thickened. Remove from heat and stir in the vanilla extract.
2 tsp vanilla extract
Add the thickened milk mixture to the prepared caramel mixture and whisk until combined.
Pour into an airtight container and allow to cool to room temperature. Cover and chill at least 8 hours.
Once chilled, pour into ice cream freezer and freeze according to manufacturer's instructions. (Mine takes about 25 minutes.)
At this point, it will be like soft serve. For a firmer ice cream, freeze 4-6 hours. Serve with a sprinkle of sea salt and enjoy!