Preheat the oven to 400 degrees. Grease a 9-inch cake pan all over the inside with a little butter.
In a large bowl, sift together the flour, baking powder, salt and sugar. Cut in the butter using a pastry cutter or two knives.
In a small bowl, whisk together the egg and milk until light and frothy.
Pour the egg mixture into the dry ingredients. Stir well until all combined. The dough will be somewhat stiff, but keep stirring until everything is incorporated.
Transfer the dough to the prepared pan. Using floured hands, gently pat it down into one even layer.
Brush the top of the coffee cake with melted butter.
Then, stir together the sugar, flour and cinnamon for the topping. Sprinkle all over the top of the coffee cake.
Bake for 20-25 minutes, until golden and a toothpick inserted in the center comes out cleanly. Let cool for five minutes in the pan.
Then, gently loosen the sides with a butter knife. Turn out onto a plate and then turn back onto a serving plate.