Place flour, cornstarch, sugar, cinnamon and salt in the bowl of a food processor. Add butter pieces and pulse 10 times or until butter pieces are about 1/2-inch big. Add ice water 1 tablespoon at a time, then pulse until dough looks ragged and holds together when pinched.
Turn dough out onto floured work surface and knead for 30 seconds. Form into a 4-inch square; wrap in plastic wrap and refrigerate for 45 minutes.
Heat oven to 400 degrees F. Place a piece of parchment on a 12 x 17-inch rimmed baking sheet and sprinkle it with flour; set aside. Place dough on floured work surface and sprinkle with flour. Roll with a floured rolling pin to about 12 x 15 inches. Transfer dough to parchment paper on baking pan. Roll up a 1/2-inch border all the way around, pressing edge tightly to adhere to dough.
Peel pears and remove core and stem, then cut lengthwise into 1/8-inch-thick slices. Layer pears over dough, overlapping them slightly. Sprinkle with butter pieces and sugar.
Bake galette at 400 degrees for about 70 minutes or until lightly browned. Meanwhile, stir together apricot preserves and 1 tablespoon water in a small bowl. Microwave for 30 seconds.
Remove galette from oven and place on wire rack to cool. Brush with apricot mixture. Makes 8 servings.