Preheat an oven to 425°F. Core and peel the pear, cutting it into about 16 wedges and then cutting those wedges in half crosswise. Toss them with the lemon juice.
Heat a 10-inch frying pan over medium-high heat. Melt 2 tablespoons of the butter. Add the pear wedges and cook, shaking the pan frequently and reducing the heat to medium-low, until the pears are cooked through, about 5 minutes. Add the cardamom and brown sugar and stir to combine, cooking until the sugar melts. Add the bourbon, if using, and cook until it doesn’t smell boozy, about 3 minutes, shaking the pan frequently.
While the pears cook, whirl the eggs, milk, flour, vanilla, and salt in a blender (or whisk until very smooth).
Transfer the pears to a plate or bowl. Add the remaining tablespoon of butter to the pan. Stir so it melts. Pour in the batter and then arrange the pears over the top (note: you can leave the pears in the pan and just pour the batter over them, but then they will all be on the bottom of the pancake). Bake until puffy and browned, about 20 minutes. At this stage, the pancake will be quite soft, for a more cooked version, reduce the heat to 375°F and bake 10 to 15 more minutes.
Serve hot, with lemon wedges for spritzing and powdered sugar for dusting, if you like.