Preheat the oven. Preheat the oven to 350°F (180°C). Lightly grease a 9-inch round cake pan.
Prepare the pears. Peel, core, and slice the pears into thick wedges. Set aside while you prepare the caramel.
Prepare the caramel topping and arrange the pears. Add the sugar and water to a small saucepan over medium heat. Cook until the sugar dissolves and the mixture turns into a golden caramel. Remove the saucepan from the heat and carefully stir in the softened diced butter, a few pieces at a time, until fully melted and combined. The caramel may bubble vigorously when you add the butter, so be careful. Pour the caramel into the prepared cake pan, tilting the pan gently to spread it evenly across the bottom. Arrange the pear slices over the caramel in an even layer, slightly overlapping them if needed.
Prepare the cake batter. In a large bowl, whisk together the almond flour, brown rice flour, cornstarch, baking powder, cinnamon, and salt until evenly combined.
In a separate bowl, beat the eggs, brown sugar, oil, and vanilla extract with an electric mixer until well combined.
Pour the wet ingredients into the dry ingredients and beat until the batter is smooth and no dry patches remain, about 1 minute. Avoid overmixing.
Assemble and bake. Pour the batter evenly over the arranged pears, gently spreading it to cover the fruit. Bake for about 40minutes, or until the cake is golden and a toothpick inserted into the center comes out clean or with a few moist crumbs.
Cool and invert. Let the cake cool in the pan until it has set enough to hold its shape but is still slightly warm. Run a thin knife around the edges, place a serving plate over the pan, and carefully invert the cake.
Allow the cake to cool before slicing and serving.