Vanilla Bean Custard:
Whisk 1/2 cup of the milk with the syrup, tapioca, salt, and the remaining 1/3 cup sugar in a medium saucepan until no lumps remain. Stir in the cream and the remaining 1 cup milk. Use a paring knife to scrape in the seeds from the vanilla bean; toss in the pod. Heat the mixture over medium-high heat, stirring with a heatproof spatula, until it begins to steam and slightly bubble at the edges.
Ladle 1 cup of the hot mixture into the yolks in a stream as you whisk the mixture to prevent the yolks from scrambling. Whisk the mixture back into the saucepan and cook at a slow simmer, stirring constantly with a spatula, until the mixture thickens enough to thickly coat a spoon, 1 to 2 minutes longer.
Set the bowl over a larger bowl of ice and water. Stir occasionally until the mixture is cool, taking care not to slosh water into the bowl. Cover and refrigerate until very cold, at least 2 hours. Transfer the bowl to the freezer for the last half hour before spinning it.
Freeze the mixture in an ice cream maker according to the manufacturer’s directions. When it is ready, transfer the ice cream to a chilled container. Cover and freeze until firm, at least 4 hours or overnight.
Put the butter and brown sugar in a mixing bowl and use a wooden spoon or a handheld electric mixer to mix until creamy. Add the egg and vanilla and mix until smooth. Stir in the flour mixture just until everything is well combined, then stir in the oats and raisins, if using.
Spoon or scoop the batter in tablespoons onto the prepared baking sheets, spacing them evenly, to make 24 cookies. Press the cookies with lightly dampened fingers to flatten them slightly—they will spread further as they bake.
Bake until the cookies are light golden around the edges, 8 to 10 minutes, rotating the pans top to bottom and front to back halfway through baking. Let the cookies cool on the pan for 5 minutes, then transfer them directly to a wire rack to cool completely, sliding a spatula under them if they do not release easily.
After the sandwiches are filled and firmly frozen, melt the chocolate with the oil in a double boiler or bowl placed over, but not touching, about 1 inch of simmering water in a saucepan until the chocolate is just barely warm and still smooth and fluid.
Vanilla Bean Custard: