3/4 cup sugar, plus extra for sprinkling
grated zest of 1 orange
2 large eggs
1/4 teaspoon salt
1 teaspoon pure vanilla extract
3/4 teaspoon cardamom
1 cup all-purpose flour
7 tablespoons unsalted butter, melted and cooled
Center a rack in the oven and preheat the oven to 350 degrees F. Butter a 9-inch cake pan or pie pan.
Pour the sugar into a medium bowl. Add the zest and blend the zest and sugar together with your fingertips until the sugar is moist and aromatic. Whisk in the eggs one at a time until well blended. Whisk in the salt and the extracts. Switch to a rubber spatula and stir in the flour, 1/4 teaspoon cinnamon and cardamom. Finally, fold in the melted butter.
Scrape the batter into the pan and smooth the top with a rubber spatula. Arrange pear slices in a circle with the top in the middle, and sprinkle with cinnamon sugar mixture.
Bake the cake for 25 to 30 minutes, or until it is golden and a little crisp on the outside; the inside will remain moist. Remove the pan from the oven and let the cake cool for 5 minutes, then run a thin knife around the sides and bottom of the cake to loosen it.