Prep the pan and oven: Heat the oven to 350°F (175°C). Line the bottom of a 9-inch round cake pan (at least 2 inches deep) with a circle of parchment.
Lightly butter the sides.
Make the caramel base: In a small saucepan, melt 4 tablespoons butter with 1/2 cup brown sugar over medium heat. Stir until smooth and bubbly, about 2 minutes. Remove from heat and stir in lemon juice, cinnamon, ginger, and a pinch of salt.
Pour into the prepared pan and spread evenly.
Arrange the pears: Fan pear slices over the caramel in tight circles, overlapping slightly. Fill any gaps with smaller pieces so the top looks full once flipped.
Whisk dry ingredients: In a medium bowl, whisk flour, baking powder, baking soda, salt, cinnamon, cardamom, and nutmeg.
Mix the wet ingredients: In a large bowl, whisk granulated sugar, brown sugar, and oil until sandy and combined. Whisk in eggs one at a time until glossy.
Add sour cream, vanilla, brandy or rum (if using), and citrus zest. Mix until smooth.
Combine batter: Add the dry ingredients to the wet and fold gently with a spatula just until no dry streaks remain. The batter will be thick and creamy.
Fill the pan: Dollop batter over the pears and spread carefully to the edges without disturbing the fruit.
Tap the pan lightly to remove air bubbles.
Bake: Bake for 38–46 minutes, until the top is golden and a toothpick inserted into the center comes out clean or with a few moist crumbs.
Cool briefly, then flip: Let the cake rest on a rack for 10–12 minutes. Run a thin knife around the edge. Place a serving plate over the pan and flip in one confident motion.
Lift off the pan and peel away the parchment.
Serve: Spoon any caramel left in the pan over the cake. Serve warm or at room temperature with whipped cream, crème fraîche, or vanilla ice cream.