Add the egg yolks to a medium bowl
Whisk the heavy cream, milk and brown sugar together in a medium sauce pot. Bring it to a simmer over low-medium heat while whisking frequently. DO NOT BOIL. If you want to keep track with a thermometer then bring it up to 190°F-195°F
Remove it from the heat immediately
Start adding ¼ cup of the hot cream mixture to the egg yolks while whisking constantly. Repeat this 6-7 times to temper the egg yolks
Add the dulce de leche to the cream mixture, reserving about ½ can for the topping
Pour the egg yolk mixture back into the heavy cream and whisk constantly until it comes back to a simmer over low-medium heat. About 8 minutes. Again, if you want to use a digital thermometer then take it to 190°F-195°F. The mixture should coat the back of a spoon
Remove it from the heat and stir in the vanilla and salt
Strain mixture through a fine mesh strainer into a large bowl
Chill the mixture in the freezer or by adding that bowl into a larger bowl filled with ice. Stir every 10-15 minutes until chilled. About 1 hour
Add the mixture to the ice cream machine and churn according to the manufactures instructions. Mine takes about 20 minutes
Pour the churned ice cream into a loaf pan then top it with remaining dulce de leche. Swirl the dulce de leche around with a butter knife to make swirls on top
Freeze overnight