Preheat and prep. Heat the oven to 350°F (180°C), conventional heat (top and bottom, no fan). Butter an 8-inch (20 cm) round cake pan, about 2 inches (5 cm) deep, and line the bottom with parchment paper.
Melt the butter and chocolate. Fill a 2-quart (2 L) saucepan with about 1 inch (2.5 cm) of water and bring it to a gentle simmer. Set a heatproof bowl on top (the bottom should not touch the water). Add the chocolate and butter and stir until smooth. Remove from heat and let cool slightly.
Prep the pear. Peel the pear and cut it in half lengthwise. Remove the core and seeds. Slice each half thinly, about ⅛ inch (3 to 4 mm) thick, and pat the slices dry.
Mix in the sugar and eggs. Whisk in the sugar in the cooled melted chocolate and butter, then the eggs, until smooth and glossy.
Fold in the dry ingredients. Sift the flour, cocoa powder and baking powder together to avoid lumps. Add them in doses with the ground almonds and salt, folding gently after each addition. Check the batter as you go: depending on the type of flour, you may need a little more or less.
Fill the pan. Pour the batter into the prepared pan and smooth the top.
Arrange the pear. Lay the slices on top in a fan, slightly overlapping. Make a fan on each side, or a flower pattern in the center.
Bake and serve. Bake at 350°F (180°C) for 25 to 30 minutes, until the cake is set and a toothpick comes out with a few moist crumbs. Cool in the pan for 10 minutes, then lift out, cut a piece and serve.
