For the filling: Preheat the oven to 325 degrees F. Place a 9-by-13-inch baking dish on a parchment lined baking sheet.
Slice the plums in half and remove the pits. Cut each half into 6 thin wedges and place in a large mixing bowl. Add the flour, honey, cardamom and salt. Toss until evenly coated. Pour into the baking dish in an even layer.
For the topping: Whisk together the flours, sugars, baking powder, salt and cardamom in a mixing bowl. Pour in the melted butter and stir together until clumps of various sizes are formed. Toss the nuts into the mixture. Pour over the fruit in an even layer, leaving some fruit exposed. Bake until the topping is golden brown and the fruit syrup is bubbly, about 40 minutes. Allow to cool slightly.
For the ice cream: Mix the ice cream, ground cinnamon and caramel sauce lightly to swirl in a bowl. Serve on the side of the cobbler.