Place ¾ cup sugar and the corn syrup in a medium heavy-bottomed saucepan. Do not stir. Place the pan over medium-high heat, and cook the mixture to a dark caramel, swirling the pan as it begins to brown to distribute the sugar. [This took me about 8 minutes.]
Add the cream; then slowly add the milk. The caramel will seize and harden, but don’t be afraid. Bring the mixture to a boil, and then simmer it, stirring, just until the caramel has dissolved.
Meanwhile, place the yolks in a large bowl with the remaining ½ cup sugar and the fleur de sel. Whisk to combine.
When the caramel cream is ready, pour a splash of it into the egg mixture to temper, whisking constantly, and then another splash or two for good measure. Then pour the tempered egg mixture into the caramel cream. Whisk thoroughly.
Pour the mixture through a fine-meshed sieve into a medium metal bowl. Place the bowl in an ice bath to cool the mixture completely. Remove the bowl from the ice bath, cover it with plastic wrap, and refrigerate overnight.
Freeze in an ice cream maker according to the manufacturer’s directions. [Put in a freezer-safe container and freeze for a minimum of 2 hours, but better if 4 or more, before serving.] Serve with additional fleur de sel sprinkled on top.