Dissolve yeast and 1 tablespoon of syrup in warm water in a small bowl, and let stand 10 minutes.
Combine flour and salt in food processor. With processor on, slowly add yeast mixture and 2 1/2 teaspoons oil through food chute; process until dough leaves sides of bowl and forms a ball.
Turn dough out onto a lightly floured surface, and knead lightly 4 times. Place dough in a large bowl coated with cooking spray, turning to coat top. Cover and let rise in a warm place (85°), free from drafts, 45 minutes or until doubled in bulk. Punch dough down; turn out onto a lightly floured surface. Roll dough into a 12-inch circle; place on a baking sheet coated with cooking spray. Brush dough with remaining oil; let dough rise 30 minutes or until puffy.
Arrange apple slices, overlapping, in a circular pattern over dough. Bake at 425° for 10 minutes. Sprinkle walnuts over apple slices, and bake an additional 10 minutes. Remove from oven; set aside.
Place 1/2 cup of syrup in a small, heavy saucepan, and cook over medium-high heat until the syrup reaches thread stage (230°). Remove from heat, and let the syrup cool slightly (about 1 minute). Drizzle syrup over apple. Serve warm.