Preheat oven to 350 degrees (325 degrees if you are using a dark metal pan). Grease 8-inch cake pan well. Set aside.
In a large bowl, add flour, baking powder, sugar, salt, and nutmeg. Whisk together to combine. In a large measuring cup, add butter and milk. Slowly add wet ingredients to the dry ingredients, whisking slowly to ensure lumps don't form. Whisk in eggs.
Pour half of the cake batter into prepared cake pan. Place the rest of the batter in a piping bag. Pipe a half-inch border around the edge of the cake pan. Fill the center with all the blackberry preserves. Use an off-set spatula to smooth the preserves into an even layer that reaches the edge of the piped ring. Pipe the rest of the batter over the top of the preserves, gently covering the preserves so they are completely sealed in the center and none is poking through. Smooth with a spatula.
Bake cake in preheat oven for 55 minutes or until the top is completely golden brown and the center is cooked through. Remove from oven and let cool for 10 minutes and then remove from panand onto serving dish.
Add sugar and cinnamon to a plate and stir to combine. Brush melted butter over the top and sides of the cake. Lift cake and roll sides in the cinnamon sugar. Sprinkle sugar mixture over the top. Serve immeditately or within a couple days. Do not store in a sealed container, or the sugar will absorb/melt into the cake. Instead, cover with foil.