Preheat oven to 425 degrees F. Place focaccia on two ungreased large baking sheets. Arrange pear slices and red onion on focaccia. Drizzle with oil; sprinkle with cheese.
Bake about 10 minutes or until heated through. Sprinkle with walnuts. To serve, cut into wedges.
In a large bowl, combine 1/2 cup all-purpose flour, 1/2 cup warm water (105 degrees F to 115 degrees F), and yeast. Beat with a wooden spoon until smooth. Cover bowl loosely with plastic wrap. Let stand at room temperature for 2 to 8 hours to ferment. Stir in 1 cup warm water (105 degrees F to 115 degrees F) and salt. Gradually stir in just enough of 3 1/4 cups all-purpose flour to make a dough that pulls away from side of bowl. Turn out onto a lightly floured surface. Knead in enough remaining flour to make a moderately soft dough that is smooth and elastic (3 to 5 minutes total). Place dough in a lightly greased bowl, turning once. Cover; let rise in a warm place until double in size (about 1 hour).
Grease two large baking sheets; set aside. Punch dough down. Cover; let rest for 10 minutes. Divide into six pieces, using oiled hands, if needed; divide between the prepared baking sheets. Press into 5-inch circles, making sure there are 2 to 3 inches of space between each circle. Brush with 1 tablespoon olive oil. Using the tips of your fingers, make 1/2-inch-deep indentations in dough. Cover with plastic wrap; let stand in a warm place for 30 minutes.