Cut kernels from the cobs to yield about 2 ¼ cups, reserving the cobs.
In a large pot, combine the corn kernels, reserved cobs, heavy cream, condensed milk, and salt.
Bring to a simmer over medium heat. Reduce to medium-low and cook, stirring frequently, until kernels are just tender (about 6 minutes).
Transfer mixture to a large heatproof bowl. Refrigerate uncovered, stirring occasionally, until fully chilled (about 3 hours).
Remove and discard the cobs, scraping any liquid back into the bowl.
Strain the mixture through a fine-mesh sieve into a large bowl, pressing on solids to extract as much liquid as possible.
Whisk in corn syrup and vanilla extract.
If desired, store the strained kernels separately in an airtight container in the refrigerator for later use as garnish.
Using an electric mixer on medium speed, beat the strained cream mixture until aerated and fluffy (about 6 minutes).
Spread mixture evenly into a freezer-safe 9 x 5-inch loaf pan.
Place plastic wrap directly on the surface.
Freeze until firm, at least 6 hours or overnight.
Scoop into bowls and garnish with reserved kernels if desired. Enjoy!