For the pears:
1) Lightly butter a 23cm round cake tin, line the bottom with baking paper, and butter the paper.
2) Put the butter, brown sugar, and lemon zest and juice in a large frying pan. Cook over medium heat, stirring, until melted. Add the pears, cover, and simmer, turning once, until the pears are soft and juicy, about 4 minutes. Pour the pears and their syrup into a strainer set over a saucepan. Set the syrup and 1 pear quarter aside.
3) Arrange remaining pears in the prepared cake tin, stem ends toward center, rounded sides down, and 0.5cm from the side. Chop reserved pear and use just enough to fill center.
For the cake:
1) Set a rack in the middle of the oven and preheat to 180C/Gas 3.
2) Scald milk in a small saucepan; keep warm.
3) Whisk flour with almonds, baking soda, baking powder, salt, cinnamon, and cloves. Beat butter with an electric mixer at medium speed until smooth, about 2 minutes. Increase speed to medium-high and gradually add caster sugar; continue beating until mixture is light and fluffy, about 4 minutes, scraping down sides of bowl. Add cocoa powder and vanilla and beat 1 minute. While mixing at medium-low speed, add eggs 1 at a time, beating well after each addition.
4) While mixing slowly, add the flour mixture in 4 additions; turn off the mixer and fold in the hot milk with a rubber spatula. Spread the batter over the pears, taking care not to disturb them. Tap the tin lightly on the counter to settle the batter. Bake until a toothpick inserted in the center comes out clean, about 50 minutes.
5) Cool cake in the pan on a rack for 20 minutes, then invert the cake onto a serving plate. Cool briefly, carefully peel the parchment paper from the top, and then cool completely.
6) To finish the cake boil the reserved pear syrup until slightly thick and lightly brush the top of the cake with syrup. Whisk a few tbsps of cocoa powder with an equal amount of icing sugar, and sift over the cake; serve.