Fill a large pot 3/4-full with water. Place the unopened can of condensed milk in the water, making sure it is covered completely, and carefully bring to a gentle boil. Reduce heat and simmer for 3 hours, adding more water as necessary. Remove from the heat and let sit until cool enough to handle. Watch the can carefully to make sure it does not start to bulge. If the can does begin to bulge, remove from the heat and let cool. Once cool, punch a small hole in the top of the can, return to the heat, and continue cooking (only partially submerged in water once the can has been pierced). When the can has cooked for 3 hours, set aside to cool completely before opening.
(If you are uncomfortable using the whole can method, you can cook the condensed milk, out of the can, over a double boiler, stirring every 5 minutes, for about 3 to 4 hours, or until it has achieved a deep golden color. Or, alternatively, purchase canned dulce de leche at your local supermarket.)
Once the dulce de leche has cooled, make the ice cream base: In a medium heavy saucepan, combine the cream and milk and bring to a gentle boil over medium heat. In a heatproof large bowl, whisk the egg yolks, 3/4 of the dulce de leche, and granulated sugar until smooth and pale. When the milk comes to a boil, whisk 1 cup of the hot cream mixture into the egg yolk-sugar mixture until smooth. Gradually add the egg mixture in a slow, steady stream to the hot cream in the pan, whisking to combine. Cook over medium-low heat, stirring constantly, until the mixture thickens enough to coat the back of a spoon, about 5 minutes. Remove from the heat and strain through a fine mesh strainer into a clean container. Cover with plastic wrap, pressing down against the surface to keep a skin from forming. Refrigerate until well chilled, about 2 hours.
Remove from the refrigerator and pour into the bowl of an ice cream machine. Freeze according to the manufacturer's instructions. When the ice cream is nearly completely churned, spoon in the remaining dulce de leche to create a swirl in the ice cream. Transfer to an airtight container and freeze until ready to serve.