Pour the sugar into a medium heavy bottomed saucepan and gently shake to level. Set over medium-low to low heat on a small burner and do not stir. After 10-15 minutes the edges of the sugar will start to caramelize. When you can see a small bit of caramelization on the edges, use a non-stick heat-proof utensil to pull the edges to the center. As the caramel cooks, stir gently to moisten and dissolve the dry sugar. Cook to a very deep, clear amber, about 30 minutes total cooking time.
When the caramel is where you want it, pour the milk and cream into the caramel in a slow, narrow stream while whisking. If the mixture seizes, don’t worry, just keep it on the heat and it will turn liquid again! Whisk until the mixture is uniform and add the salt. Remove from the heat.
In a medium bowl, whisk the yolks for 1 minute until slightly lighter in color. Whisk 1/3 of the hot cream mixture into the yolks, then whisk the whole thing back into the saucepan.
Return the saucepan to medium-low heat and cook, while stirring, to 170F. The mixture will be slightly thickened and will cling to the back of a spoon. Remove from the heat and stir in the vanilla.
Place a fine mesh sieve over a clean bowl and strain the mixture through. DIscard any solids and cover the bowl to prevent a skin from forming. Allow to cool to room temperature, then refrigerate for at least 4 hours and up to overnight.
Churn in an ice cream maker according to the manufacturer’s directions, then pack into containers and freeze until firm. Enjoy!