Shake coconut milk in cans before opening; pour ¼ cup (60 mL) into bowl. Set aside.
In medium, heavy-bottomed saucepan, whisk remaining coconut milk with sugar until smooth. Bring to simmer over medium-high heat; stirring occasionally.
Whisk tapioca in bowl with reserved coconut milk; whisk into saucepan. Cook, stirring often, until slightly thickened, about 3 minutes. Stir in vanilla and salt.
Strain through fine-mesh sieve into square metal cake pan. Refrigerate until chilled, uncovered and stirring occasionally, about 1 hour. Transfer to freezer; freeze until almost solid, about 1 ½ hours.
Break up with spoon and transfer to food processor; puree until smooth. Transfer ice cream into airtight container; return to freezer until firm, 3 to 4 hours (or up to 1 week). If using ice cream machine, freeze according to manufacturer’s instructions.