Peel the lime avoiding the pith to obtain big pieces of zest.
Place egg yolks in medium bowl and set aside. Place coconut milk and vanilla in a large bowl and set aside.
Combine half the zest with the milk, salt, and sugar in a saucepan. Set over low heat and bring to simmer stirring occasionally to dissolve sugar. Off heat.
In a bowl, stir together the egg yolks and add a couple shots of bitters if using. Gradually add some of the warmed milk mixture, stirring constantly as you pour. Pour the warmed yolks back into the saucepan.
Cook over low heat, stirring constantly and scraping the bottom until the custard thickens enough to coat the back of a wooden spoon.
Strain this mixture into the coconut milk. Stir in the remaining zest and allow to steep. Chill thoroughly, then remove the zest and freeze in your ice cream maker according to the manufacturer's instructions.