Preheat oven to 350°. Butter and flour a 9-in. tube pan* or 10- to 11-cup nonstick Bundt pan, knocking out excess flour.
Make topping: Combine brown sugar, walnuts, and cinnamon in a small bowl. Slice pears lengthwise 1/3 in. thick if using tube pan or chop if using Bundt pan.
Make cake: Beat butter and granulated sugar with a mixer until fluffy. Add eggs one at a time, mixing well and scraping inside of bowl after each addition. Scrape seeds from vanilla bean and add to bowl (save pod for another use). Add syrup and sour cream; beat to combine.
Combine dry ingredients. Add to batter and beat on low speed until blended; batter will be thick.
Sprinkle half the nut mixture in pan, then arrange half the pears on top. Spoon half the batter over pears and spread evenly. Repeat layers. Bake until a toothpick inserted in center comes out clean, 55 to 60 minutes for a tube pan, 45 minutes for a Bundt pan.
Let cool in pan on a rack about 45 minutes. Loosen cake from sides of pan with a small, slender spatula and invert onto a plate. If any toppings stick in pan, loosen with spatula and replace on cake.
*You can order a 9-in. tube pan ($18) from amazon.com.
Make ahead: Up to 1 day, chilled; set on a baking sheet, wrap in foil, and rewarm in a 350° oven about 15 minutes.
Note: Nutritional analysis is per serving.