Heat oven to 350°F and butter a 9-by-5-inch baking dish. Set aside.
In a large bowl, combine oats, pistachios, cardamom, ginger, baking powder, and salt, and stir.
In a medium bowl whisk crème fraîche, milk, egg, honey, and vanilla. Pour mixture into dry ingredients, and stir to combine. Gently fold in raspberries.
Pour mixture into buttered baking dish, brush the top of the oatmeal with melted butter, and bake for 25 to 35 minutes. Cool slightly, and serve with an extra dollop of crème fraîche if you like.