It becomes obvious after you've made applesauce two or three times that peeling and coring the apples is unnecessary. Once that discovery has been made, it becomes very apparent that applesauce is easy to prepare fresh whenever you want. And what better time could there be to make applesauce than now, when local cooking apples from the Shenandoah Valley are fresh, abundant and relatively inexpensive?

Fresh applesauce can be served as a simple, quick dessert for family meals, as it has been for generations, or it can accompany meats and poultry. When serving applesauce with game or pork, try the variation flavored with horseradish. Otherwise, serve the applesauce plain or flavored with spices, citrus rinds, ginger or nuts.

In this recipe, the apples are cooked unpeeled and uncored, and are then pressed through a strainer to form a smooth sauce. This is the way applesauce should be -- smooth. Using whole cut-up apples not only saves time and effort, but cooking with the skin adds both flavor and a gentle pink blush to the sauce.

If you want a chunky applesauce, the apples can be peeled and cored, cut into large dice and cooked until tender, using twice the water and sugar. But then you'll have more of an apple compote than a true applesauce.

However you choose to make it, freshly cooked applesauce is the sign of a caring cook, always a welcome sign at the dinner table. SMOOTH AND EASY APPLESAUCE (Makes about 2 1/2 cups) 8 large (about 3 pounds) cooking apples, such as staymans or jonathans 1/4 cup sugar 1/4 cup water

Cut each apple into 8 chunks and place in a large pot with the sugar and water. Cover and set over medium-high heat until the pot fills with steam, then reduce the heat to medium-low and cook, still covered, until apples are very tender, about 20 minutes.

Press the apples through a fine-mesh strainer to remove the skins, seeds and cores, discarding any juices that have accumulated around the apples.

Refrigerate until serving time. VARIATIONS

Spiced applesauce: Add a half teaspoon of ground cinnamon and a couple of healthy dashes of nutmeg to the warm applesauce and mix well.

Buttered applesauce: To enrich fresh applesauce or add flavor to winter stored apples, stir 4 tablespoons of unsalted butter into the warm applesauce, whether spiced or plain.

Applesauce with horseradish: Add 3 to 4 tablespoons of squeezed dry prepared white horseradish to the warm applesauce and mix well.

Flavored applesauce: Add the grated zest of a lemon and an orange to the warm applesauce and mix well, using either plain or spiced applesauce.

Gingered applesauce: Add 1/3 cup very finely chopped preserved ginger to the warm applesauce, whether plain or spiced, and stir together.

Applesauce with pecans or walnuts: Stir half a cup of roughly chopped pecans or walnuts into the warm applesauce, using plain, spiced, or gingered applesauce.