Preheat the oven to 350°F. Butter a 9-inch springform pan and line the base with parchment paper. Set aside.
In a stand mixer fitted with the paddle attachment, cream butter and sugar until light and airy, about three minutes. In a separate medium-sized bowl, whisk dry ingredients together. Set aside.
Stop the mixer and, using a spatula, scrape down the sides of the mixing bowl. Turn the mixer to medium low and add yogurt and vanilla extract; then add eggs one at a time, beating well after each addition.
Turn the mixture to low and then slowly add the dry ingredients, taking care to not overmix.
Using an offset spatula, evenly spread the batter into the prepared cake pan.
Clean and peel the pears. Slice the pears ¼-inch thick and arrange on top of the cake in a concentric circle, overlapping them a bit. Sprinkle with turbinado sugar.
Bake for 55-65 minutes, or until a skewer comes out clean and the top of the cake springs back to the touch. Remove from the oven and let cool in the pan for about 10 minutes. Remove the sides of the springform pan and let cool completely.
While the cake is baking, make the rum toffee sauce. Place the brown sugar and water in a medium saucepan set over medium-high heat, whisking until the sugar crystals dissolve. Once the mixture has reached a rolling boil, add butter and cream. Return to a boil while whisking constantly for at least four minutes.
Remove from heat and stir in the rum, vanilla, and salt. Set aside to cool to room temperature.
Serve the cake while still slightly warm and drizzle the toffee sauce on it immediately before serving.
Enjoy!