In a medium saucepan, combine the half and half, one-third of the heavy cream, and all the allulose, salt, and mint. Warm over medium-high heat until steaming hot with small bubbles around the edges; do not boil. Remove from the heat, cover, and let infuse for 1 hour.
Strain the infused cream through a fine mesh strainer set over a bowl, then firmly press down on the mint with a rubber spatula to extract the maximum amount of mint flavor and color. Discard the mint. Pour the strained cream mixture back into the saucepan, then reheat over medium heat just until steaming.
In a medium bowl set in a coiled kitchen towel to prevent slipping, whisk together the egg yolks. Very slowly pour about one-third of the just-steaming cream into yolks, whisking constantly, to gently temper the yolks. When combined, pour the warmed yolk mixture back into the saucepan with remaining infused cream. Stir the custard to combine.
Make an ice bath by partially filling a large bowl with ice and cold water. Set a slightly smaller bowl within it so that it easily rests in the water without getting the inside of the bowl wet. Pour the remaining heavy cream into the smaller bowl, then set the mesh strainer over the top. Set aside.
Stirring constantly, cook the custard over medium heat until it’s as thick as a thin gravy or reads around 170°F (75°C) on an instant-read thermometer, 2 to 3 minutes.
Immediately pour the mixture through the mesh strainer set over the iced cream. Stir the mixture while it’s nestled in the ice bath until cool, 4 to 5 minutes.
Refrigerate the mixture for at least 6 hours, preferably overnight, then freeze it in your ice cream maker according to the manufacturer’s instructions.
Transfer the churned ice cream to an airtight storage container and freeze it for 3 to 4 hours before serving.