Preheat the oven to 300°F, with an oven rack in the center position.
In a mixing bowl (using a wooden spoon) or in the large bowl of an electric mixer, cream the butter with the almond extract until soft. Beat in the 1cup of coconut.
Sift together the flour, cornstarch, and confectioners’ sugar. Beat the flour mixture into the creamed mixture. Form the dough into a large ball, wrap it in plastic wrap, and refrigerate it for at least an hour, or until it is firm. (The dough may be refrigerated for up to two days.)
When firm, remove the dough from the refrigerator, shape it into 1-inch balls, and place them about 1½ inches apart on an ungreased baking sheet. Dip a table fork into flour and flatten each cookie slightly, pressing it once.
Bake the cookies in the center of the preheated oven until their edges are lightly browned, about 20 minutes. Cool on the sheet about 5 minutes, then remove them to racks to cool completely.
Add the optional trimming: Spread a little of the apricot preserves around the edge of each cookie and sprinkle a little of the additional ⅓cup of coconut over the jam. Store the cookies in a tightly closed container at room temperature for a few days, or refrigerate them for up to several weeks.