For the Dulce de Leche:
For the Ice Cream:
To make the dulce de leche, preheat the oven to 425° Fahrenheit.
Pour one can of sweetened condensed milk into a glass pie plate or shallow baking dish. We used an 8-by-8" glass baking pan. Stir in some flakes of fleur de sel.
Place the glass baking plate into a larger roasting pan. Cover the glass baking dish very tightly with aluminum foil. Then, fill the large roasting pan with hot or boiling water enough to reach halfway up the sides of the glass dish.
Bake the entire thing for 1 to 1 1/4 hours making sure to check the water level and refill if it gets too low.
When you pull out the pan, allow to cool and then whisk the now caramelized sweetened condensed milk until smooth. It's ok if it's not perfectly smooth, it will still taste delicious. Just try to stop yourself from taking a spoonful.
Store in the refrigerator until ready to add to the ice cream. If you want to eat the dulce de leche over ice cream or apple pie (or with a spoon by yourself while watching 'Sex in the City' reruns) microwave the sauce gently to soften. Really, it is that easy.
While the dulce de leche is cooling, make the ice cream base.
In a bowl, whisk together the egg yolks, sugar, vanilla, and salt. Pour the milk and cream into a small saucepan warm over low heat until hot, but not boiling. Stir with a wooden spoon, scraping the bottom of the pan to prevent sticking. Very slowly pour the hot cream into the eggs to temper them and whisk until smooth. Don't worry if it's a bit lumpy. You're going to sieve the whole thing at the end.
Return the mixture to the saucepan and cook over medium-low until thick and bubbling around the edges. The custard will coat a wooden spoon. Use your instinct. It will feel thicker when you are stirring it.
Strain the custard through a fine-mesh sieve into a bowl. Cover and chill for at least 3 hours or overnight.
Pour the cream into the canister of an ice cream maker. Freeze according to manufacturer’s instructions. When the ice cream is the consistency of frozen whipped cream, right before the ice cream is done, add thick dolops of dulce de leche, allowing the caramel to mix into the ice cream ever-so-slightly.
Then, cover with plastic wrap, and freeze in the refrigerator’s freezer for at least 3 hours until ready to serve.
This would be fabulous with apple pie or ginger cake or anything.