Prepare a 9 × 5-inch loaf pan or freezer-safe container.
Measure all caramel ingredients before beginning.
Heat granulated sugar in a heavy-bottomed saucepan over medium heat until melted and deep amber.
Carefully add butter and whisk until incorporated.
Slowly add warm heavy cream while whisking carefully.
Remove from heat and stir in sea salt.
Transfer caramel to a heat-safe container and cool completely.
Beat 2 cups cold heavy cream until medium peaks form.
In another bowl, combine sweetened condensed milk, vanilla, and a pinch of salt.
Fold one-third of the whipped cream into the condensed milk.
Gently fold in the remaining whipped cream in two additions.
Spread one-third of the ice cream base into the prepared container.
Drizzle with cooled salted caramel.
Repeat with another layer of ice cream and caramel.
Add the remaining ice cream mixture.
Drizzle additional caramel over the surface.
Swirl gently with a butter knife only a few times.
Cover tightly.
Freeze for at least 6 hours or overnight.
Let stand for 5–10 minutes if necessary before scooping.
Serve with reserved caramel and optional flaky sea salt.