Preheat oven to 350ºF (180ºC).
In the bowl of a mixer, cream together the butter and sugar. Add vanilla extract and egg, continue mixing until smooth.
In a separate bowl, mix together the flour, baking powder and salt. Add one half of it to the mixer, and when mostly combined, start pouring in the milk. Once the milk is mostly combined, add the remaining flour.
For the filling: in a small bowl, mix the softened butter, flour, sugar and cinnamon until you get a grainy consistency.
For the crumble: Mix the softened butter, oats, flour, brown sugar and cinnamon with your fingers or a fork until the crumbs form.
Grease a large loaf pan. Pour in half of the cake batter and spread. Sprinkle in the filling and cover with the other half of the cake batter. Sprinkle the crumble over the top and press lightly so it adheres.
Bake in preheated oven for 45-50 minutes, until a toothpick inserted into the center comes out clean.