Preheat oven to 350°F. Melt 4 tablespoons of the butter in a 12-inch cast-iron skillet over medium heat. Add brown sugar and cook, stirring, until the mixture is very smooth, about 3 minutes. Remove from the heat and sprinkle cranberries evenly over the brown sugar mixture. Arrange apple and pear slices in a mosaic pattern over the sugar mixture, double-layering the fruit slices if needed to fit them all. Set aside.

In the bowl of an electric mixer, beat remaining 10 tablespoons butter with cane sugar until fluffy. Beat in eggs and yolk one at a time. In a separate bowl, whisk together flour, cinnamon, baking powder, baking soda and salt. On low speed, beat flour mixture into butter mixture in 3 additions, alternating with additions of buttermilk and scraping down the sides of the bowl occasionally. Pour batter into the skillet over the fruit, smooth the top, and bake in the middle of the oven until the top is golden and the cake springs back when pressed in the center with your fingertip, 45 to 50 minutes.

Cool the cake in the skillet 15 minutes. Run a knife around the edge of the skillet to loosen the cake, then place a large round platter upside-down over the skillet. Protecting your hands with oven mitts, grasp the skillet securely and invert. Lift off the skillet; use a fork to replace or straighten any fruit that has become dislodged. Serve warm or room temperature.