Preheat the oven to 350°. Butter a 10-inch cast iron skillet.
Whisk together the all purpose flour, graham flour, baking powder, salt, and baking soda in a small bowl.
In a large bowl, beat butter and brown sugar with an electric mixer on medium until light and fluffy, about 2 minutes. Add the eggs, one at a time, followed by the vanilla extract.
Whisk the flour mixture and buttermilk into the butter-sugar mixture in alternate additions, beginning and ending with the flour. Fold in 1½ cups of the raspberries and the chocolate. Transfer the batter to the prepared pan and smooth the top. Top with the remaining cup of raspberries and sprinkle with the granulated sugar. Bake until a toothpick inserted into the center comes out with moist crumbs attached, 35 to 40 minutes. Serve warm or at room temperature.