Preheat the oven to 350°F. Butter a 9-inch springform baking pan (see Note)
Make the Topping: In a small bowl combine the brown sugar, flour, cinnamon, and salt. Add the butter and using your fingers or a pastry cutter or two knives combine everything until the butter is cut into the dry mixture, and the whole thing is quite crumbly (it should not be a paste; there should be little pieces of butter throughout).
Make the Cake: In a medium bowl, combine the flour, baking powder, cinnamon and salt.
In a large bowl , beat the butter and the sugar together with an electric mixer until light and fluffy. Add the egg and beat until incorporated, then beat in the vanilla. Add half the flour mixture, and beat just until almost incorporated, then beat in the milk just until blended, then repeat with the rest of the flour, beating just until everything is combined, but not any more than that. Gently fold in 2 cups raspberries, then spread the batter into the prepared pan (it will be thick). Sprinkle the remaining cup of raspberries on top, then sprinkle the crumb topping evenly over the raspberries.
Bake for 45 to 50 minutes, or until golden brown. A wooden skewer inserted into the middle might have some berry stuck to it when you pull it out, but there should not be any uncooked batter.
Let cool on a wire rack for 15 minutes, then release it from the pan and continue to cool it on the bottom part of the pan on the wire rack.
If you are making the vanilla drizzle, combine the confectioners' sugar, vanilla, and water in a cup or small bowl. Use a teaspooon to drizzle the icing over the cooled cake.
Notes
I like the idea of mixing some of the berries fully into the cake batter, but sprinkling some directly on top as a bright juicy layer right underneath the topping, with little pops of color peeking through the crumbs. Skip the drizzle if it’s just that one extra step, but it does add a bakery finish to the whole thing.