Butter a 9-inch round baking pan.
To make the fruit topping, put the sugar and water in a heavy saucepan (one with a tight-fitting lid) and stir until the sugar dissolves. Bring the mixture to a boil over medium heat, then cover and cook for 2 minutes. (Covering in this way allows the steam to wash down the sides of pan, which will prevent any sugar crystals from forming.) Uncover the saucepan and continue to boil the sugar, gently and slowly swirling the pan as needed to cook the caramel evenly, until it becomes a dark amber color. Occasionally wash down the sides of the pan with a pastry brush dipped in cold water. Carefully pour the caramel into the prepared pan and allow it to harden. The pan will be very hot from the sugar, so take care in moving it if you need to. Fan the pear slices on top of the caramel in a circle around the perimeter, filling in the center with the remaining slices.
Preheat the oven to 350°F.
To make the cake, place the butter and chocolate in a small saucepan over low heat and melt, stirring occasionally. Sift the flour, cocoa, baking soda, and salt together in a bowl. Transfer the melted chocolate to a mixing bowl or the bowl of a stand mixer and add the sugar. Using a handheld mixer with beaters or a stand mixer with the paddle attachment, beat on medium speed for about 3 minutes, until light and fluffy. Add the eggs one at time, scraping down the sides of the bowl after each addition. Stir in the vanilla. Stir in the flour mixture in three additions alternating with the milk in two additions, beginning and ending with the flour and scraping down the sides of the bowl occasionally.
Pour the batter into the prepared pan and bake in the middle of the oven for 40 to 45 minutes, or until the cake bounces back slightly when touched. Cool on a wire rack for 15 minutes, then invert the cake onto a plate, leaving the pan on top of the cake for 5 minutes before you remove it. Serve the cake warm, topped with a small dollop of Chantilly cream or a scoop of Vanilla Bean Ice Cream.
Storage: Wrapped in plastic wrap, the cake will keep at room temperature for up to 3 days.