Grilled Pineapple with Kahlua Dulce de Leche

2 (14 ounce) cans sweetened condensed milk
1/3 cup Kahlua
1/4 teaspoon vanilla extract
1/2 ripe pineapple, preferably golden
Vanilla ice cream, as needed

Preheat oven to 425 degrees F.

Pour sweetened condensed milk into a 9-inch deep-dish pie plate and cover with foil. Put pie plate in a roasting pan and add enough hot water to pan to reach halfway up side of pie plate. Bake milk in middle of oven until thick and golden, about 1 1/2 hours. Carefully remove pie plate from pan and cool completely.

Add Kahlua and vanilla extract to cooled caramelized milk, whisk until smooth, and season with salt. (The dulce de leche may be made 2 days ahead and chilled, covered.)

Prepare a grill or grill pan. Cut the pineapple lengthwise through leaves, keeping leaves attached, into 4 wedges. Grill the pineapple wedges, cut-side down, until just charred, about 2 minutes on each cut side. Divide the wedges among plates, put a scoop of ice cream next to each, and drizzle with the dulce de leche.