This pudding is delicious with almost any fruit. Substitute fresh peach or apricot wedges for the nectarines, or serve with a warm fruit compote or stewed fruit.
Combine tapioca, sugar, 2 tablespoons honey, salt, eggs, and milk in a medium saucepan, and whisk to combine. Let stand, without stirring, for about 5 minutes. Cook over medium heat, stirring, until mixture comes to a full boil.
Transfer to a medium bowl set over a bowl of ice water. Let stand to cool, stirring occasionally, 12 to 15 minutes. When cool, pudding can be refrigerated for up to 1 day before serving.
Meanwhile, heat remaining 2 tablespoons honey in a medium skillet over medium heat. Add nectarine wedges, and sprinkle with ground ginger. Cook until fruit is just tender, 2 to 3 minutes. Divide the pudding among four dishes and spoon nectarines over. Top each with a sprig of mint, if desired.