In a mixing bowl, whisk the egg yolks with half of the sugar until the mixture is pale and fluffy.
In a saucepan, heat the milk and the remaining sugar until hot, about 175° F, but not boiling.
Temper the egg yolks: While whisking constantly, slowly pour the hot milk in a thin stream into the egg yolk and sugar mixture. This will temper the eggs so they don’t curdle.
Return the mixture to the pan and heat until it reaches 180° F, stirring constantly. Do not allow the mixture to boil.
Remove from heat and whisk in the ube paste and extract. Stir in the cream and salt.
Strain the mixture through a fine mesh strainer.
Allow mixture to cool. Chill in the refrigerator until it reaches 40 degrees F, about 4 hours or overnight.
Churn in ice cream machine until a soft serve consistency, about 20 minutes. Transfer to a chilled container, cover with plastic wrap and press onto the surface of the ice cream.
Freeze until firm, about 4 hours.
Ice cream can be stored in freezer up to 5 days.