Butter a 10 1/2-inch round baking dish or pie plate. Fan pear slices out in a single layer in the bottom.
Beat eggs and sugar together using an electric mixer fitted with a paddle attachment on medium speed until light and fluffy, about 3 minutes. Mix in heavy cream, flour, kirsch, lemon zest, vanilla extract, cardamom, and salt on low speed until batter is smooth. Set batter aside to rest, about 15 minutes.
Pour batter over the pears in the baking dish.
Bake in the preheated oven until set and golden brown, 40 to 45 minutes. Let cool briefly, about 15 minutes. Serve warm, sprinkled with confectioners' sugar.
