Core and slice them somewhat thick, about 3-4 mm. Melt butter in 10-inch cast iron skillet
Simmer over moderate heat, stirring, 4 minutes to prevent burning.
Arrange pears on top of sugar mixture in any pattern you like, overlapping pieces slightly.
Sift together flour, cardamom, and salt.
Beat butter in a large bowl until light and fluffy gradually beat in granulated sugar
Add eggs, 1 at a time, beating well after each addition
Add half of flour mixture
Add remaining flour mixture
Spoon batter over pear topping and spread evenly. bake cake in middle of oven until golden and a tester comes out clean, about 45 minutes at 350 degrees
Let cake stand in skillet 5 minutes
Invert a plate over skillet and invert cake onto plate (keeping plate and skillet firmly pressed together). replace any pear stuck to botton of skillet
Serve cake just warm or at room temperature