Program the oven to 400°F.
Cut the plums in half, remove the pith from them and place them onto a rimmed parchment-lined baking sheet.
Sprinkle the brown sugar, sea salt and bake them for 20 minutes until they are tender and the juices have been released.
Let the roasted plums sit for 5 minutes and place the minced ginger, heavy cream, half and half, granulated sugar, vanilla extract, and orange zest into a saucepot.
Heat the cream mixture for 4-5 minutes until the sugar crystals dissolve, then pour it into a sieve set over a bowl.
Place the roasted plums into a blender along with 1/2 cup of ginger-infused cream and blend it into a smooth puree.
Pour the pureed plums into a sieve set over a bowl, and throw away the pulp. Stir in the ginger-infused cream, cover it, and refrigerate it for at least 4-5 hours or overnight.
Churn the roasted plum ice cream base into an ice cream machine according to the manufacturer's instructions.
Transfer the roasted plum ice cream into an airtight freezer-safe container and freeze it for 3-4 hours.