Preheat oven to 350°. Generously butter a 9-in. cake pan and arrange pear slices in a pattern on the bottom of pan. Set aside.
Bring 1 cup granulated sugar and 1/2 cup water to a boil in a 10-in. frying pan (not nonstick) over medium-high heat. Lower heat to maintain a steady simmer and cook, undisturbed, until mixture starts to brown (swirl pan to help mixture brown evenly). When mixture turns a medium amber color, add 1/2 cup pecans and cook until fragrant but not burning, about 30 seconds. Remove from heat and slowly stir in bourbon and 1/2 tsp. salt. Pour over pears in buttered pan.
Put 3/4 cup butter, the brown sugar, and remaining 1/4 cup granulated sugar in a large bowl. Beat until smooth and a bit fluffy, about 3 minutes. Add eggs one at a time, beating well after each addition. Beat in vanilla, baking powder, baking soda, and remaining 1/2 tsp. salt. Add half of the flour and beat until combined. Then beat in half of the yogurt. Repeat with remaining flour and yogurt. Stir remaining 1/2 cup pecans into batter (it will be thick).
Drop spoonfuls of batter over pears and sauce and spread evenly. Bake cake until golden and a toothpick inserted in the center comes out clean, about 45 minutes. Let cool on a rack 15 minutes. Run a knife between cake and pan sides and invert cake onto a plate or serving platter. Serve warm or at room temperature.
Note: Nutritional analysis is per serving.