Cut the Asian pears in half vertically. Use a small spoon to scoop out the core. Put the 4 halves in a pot large enough to fit the pears in a single layer.

Cover the pears with the pomegranate juice and plum wine. Add more juice and wine if the pears are not completely covered. Bring to a boil, then lower the heat and simmer for 20 minutes. Take the pot off the heat and let the pears come to room temperature in the pot. Remove the pears and juice from the pot and put in a bowl. Cover and refrigerate overnight.

Preheat a grill to high.

When you're ready to serve the pears, dry each half thoroughly using paper towels. Put the sugar on a shallow plate and dip the flat side of each half in the sugar. Put each pear half, flat side down, on a very hot grill and grill until the sugar is brown and bubbly.

Transfer the pears to serving plates, flat side up. Put a scoop of vanilla ice cream in the middle of each pear and garnish with mint.