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½ pineapple

2 large peaches

1. Start a grill; the fire should be quite hot and the rack positioned 4 to 6 inches from the heat source. Combine the sugar, ginger, and ½ cup of water in a saucepan over medium heat. Bring to a boil and simmer for 3 minutes. Remove from the heat and let sit while you prepare the fruit.

2. Do not peel the bananas; cut them into 2-inch-long chunks and make a shallow vertical slit in the skin to facilitate peeling at the table. Peel and core the pineapple, then cut it into 2-inch chunks. Pit the peaches and cut them into large chunks.

3. Skewer the fruit. Strain the syrup and brush the fruit lightly with it. Grill the fruit until the pineapple is nicely browned, 2 to 4 minutes per side. As it is grilling, brush occasionally with the syrup.

4. When the fruit is done, brush once more with syrup; serve hot or warm.

LIME GRANITA

MAKES 4 SERVINGS

TIME: AT LEAST 2 HOURS, LARGELY UNATTENDED

UNLIKE ALMOST EVERY other frozen dessert, granitas take no special equipment. They do take some time, however, and do not keep well, so timing is important. Figure two to three hours for this, start to finish.

⅔ cup sugar, or to taste

1 cup fresh lemon or lime juice

1 tablespoon minced or grated lemon or lime zest

1. Mix the sugar with ⅔ cup of boiling water and stir to dissolve. Add another cup of water and combine with the citrus juice and zest. Taste and add more sugar if necessary.

2. Pour the prepared mixture into a shallow metal or glass pan or bowl. Freeze for about 30 minutes, or until ice crystals begin to form at the edges. Gently stir the crystals back into the liquid, not breaking them up entirely; a large fork is a good tool for this task.

3. Continue to stir and break up clumps of crystals every half hour or so. When the entire mixture has the texture of soft crushed ice, it’s ready to serve. Serve immediately or continue to stir every half hour or so until ready to serve.

PINEAPPLE-GINGER SORBET

MAKES 4 SERVINGS

TIME: 10 MINUTES, PLUS TIME TO FREEZE

A SPECIAL COMBINATION, decidedly Asian. Use fresh ginger if at all possible.

½ cup sugar

1½ teaspoons very finely minced peeled fresh or candied ginger or ½ teaspoon dried ginger, or to taste

1 medium pineapple, peeled, cored, and pureed in a food processor (about 2 cups)

Whisk the sugar and ginger into the puree and freeze in an ice cream machine, according to the manufacturer’s directions. This is best served straight from the machine or after no more than an hour or two in the freezer.

COCONUT SORBET

MAKES 1 QUART

TIME: 5 MINUTES, PLUS TIME TO FREEZE

IF YOU HAVE an ice cream machine, this is one of the fastest, easiest, most satisfying desserts you can make.

3 cans coconut milk (about 1 quart)

1 cup sugar, or to taste

2 teaspoons vanilla extract

1. Combine the coconut milk with the sugar and taste; add more sugar if you like. Add the vanilla and stir.

2. Freeze in an ice cream machine according to the manufacturer’s instructions. Serve as soon as possible after making or freeze and let “warm” in the refrigerator for 30 minutes before serving. Best the day it is made.

COOKIE DOUGH

MAKES ABOUT 4 DOZEN

TIME: 30 MINUTES

COOKIES ARE ALWAYS easy to make, but even they can use streamlining. One solution is to whip up a single dough in a food processor and finish it in different ways. This basic dough is great plain (with white sugar or brown or even molasses), but it can be varied with ginger or a mix of spices, chocolate chips, or orange. Or with one batch of dough you can make four different types of cookies—add lemon juice and zest to one-fourth of it, for example, chopped walnuts to the second, raisins to the third, and coconut to the fourth. Finally, it can produce rolled-out, cut, and decorated cookies; just chill it first to make it easier to handle. You might call this “the mother of all butter cookies.”

Make these with more flour and they’re cakey; use more butter and they’re delicate, with better flavor; here, I go for the second option.

1½ cups all-purpose flour

½ cup cornstarch

¾ cup