Core the pears and cut each into eight sections lengthwise. Combine the wine, nectar or juice, vanilla, and spices in a saucepan.
Put in the pears and bring to a simmer. Cover and simmer over low heat until the pears are just done—fork-tender but still firm. This will take from 10 to 20 minutes, depending on how firm the pears are in the first place.
Combine the arrowroot or cornstarch with just enough water to dissolve it. Stir into the liquid in the saucepan and simmer, uncovered, until thickened. Remove from the heat and cover.
Just before serving, combine the chocolate chips and about 1 tablespoon of water in the top of a double boiler or a small aluminum bowl perched atop a saucepan filled with a small amount of water. Heat until smoothly melted. You can also do this in a microwave — combine the chocolate and water in a heatproof bowl and start with 40 seconds. Add a bit more time if need be, stirring each time until the chips are smoothly melted.
Arrange the pear slices in 3 to 4 dessert bowls, depending on how many you're serving. Divide the cooking liquid between them.
Dip a teaspoon into the melted chocolate and drizzle over the pears in a zigzag pattern, repeating until the chocolate is used up. To make a neater drizzle pour it into a small zip top plastic bag, make a tiny snip in the corner, and use like a piping bag to do the drizzle. Serve at once.