Preheat oven to 350°. Grease a 10-inch tube pan, and dust with flour.
Combine 3 cups flour, baking powder, baking soda, 1/2 teaspoon cinnamon, and kosher salt in a medium bowl. Mix 1/3 cup sugar with remaining 1/2 teaspoon cinnamon and 2 tablespoons flour mixture in a large bowl. Add pears to large bowl, and toss gently.
Beat butter in a large bowl at medium speed with an electric mixer until creamy. Gradually beat in remaining 2 cups sugar, and continue beating until light and fluffy. Scrape sides of bowl. Add eggs, 1 at a time, beating well after each addition. Scrape sides of bowl. Gradually beat in remaining flour mixture with mixer on low speed until blended. Add orange juice and extracts; beat until smooth.
Spoon one-third of batter into prepared pan, and smooth over bottom. Top with half of pears, keeping within edges of batter. Spread another layer of batter, and top with remaining pears. Top with remaining batter to cover pears.
Bake 1 hour 5 minutes to 1 hour 15 minutes or until cake is golden brown and a wooden pick inserted in center comes out clean. Transfer to a wire rack, and let cool 1 hour. Run a knife around edges of pan and center tube. Invert onto a plate. Dust with powdered sugar, if desired.
*For testing purposes, we used the sweet Starkrimson pear, available July through February.
**Remove eggs from refrigerator, and place in a bowl for 30 minutes.
Matzoh Ball Gumbo: Culinary Tales of the Jewish South