Preheat the oven to 350˚. Butter the bottom and side of a 9-inch round cake pan. Toss the pear wedges with 1 tablespoon lemon juice in a large bowl; set aside. Bring 3/4 cup granulated sugar, the water and remaining 1 teaspoon lemon juice to a simmer in a medium skillet over medium heat, stirring occasionally. Simmer, without stirring, until amber, 6 to 7 minutes. Remove from the heat and stir in 2 tablespoons butter. Pour the caramel into the prepared pan, tilting to coat the bottom. Let cool, then top with the pears in a circular pattern.
Whisk the flour, baking powder, baking soda, salt and cardamom in a medium bowl. Combine the milk, sour cream and maple extract in a large liquid measuring cup and stir until smooth. Beat the remaining 1 stick butter, 1/2 cup granulated sugar and the maple sugar in a large bowl with a mixer on medium-high speed, scraping down the bowl occasionally, until light and fluffy, 3 to 5 minutes. Beat in the eggs one at a time.
Reduce the mixer speed to medium and beat until thickened, about 1 minute. Reduce the mixer speed to low and add the flour mixture in three batches, alternating with the milk mixture in two batches. The batter may look slightly curdled; keep beating and it will smooth out.
Pour the batter into the pan over the pears and smooth the top. Bake until the top of the cake is a deep golden brown and a toothpick inserted into the center comes out clean, 55 to 65 minutes. Transfer to a rack and let cool 20 minutes in the pan. Run a thin knife around the edge of the cake to loosen, then invert onto a serving plate and let cool completely.