Put the granola, brown sugar, flour, cardamom, cinnamon, and butter in a bowl, mix the ingredients with finger tips until the butter is well incorporated.
Arrange the pears, skin-side down in a heavy 9 by 9-inch baking dish. Spoon and press the granola mixture on the pears. Place the dish in the oven until the granola mixture is golden brown and pears are tender, approximately 30 minutes.
Remove the baking dish from the oven and serve with vanilla ice cream.