In a large mixing bowl, cream together the softened butter and granulated sugar until light and fluffy. Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.

In a separate bowl, whisk together the flour, baking powder, and salt. Gradually add the dry ingredients to the wet mixture, alternating with the milk. Mix until just combined.

Gently fold in the sliced plums into the cake batter, being careful not to break them up too much.

In a small bowl, combine the flour, brown sugar, softened butter, and cinnamon. Use your fingers or a fork to mix until crumbly. If using oats, stir them in as well.

Pour the cake batter into the prepared cake pan and spread it evenly. Sprinkle the crumble topping generously over the batter.

Bake in the preheated oven for 40-45 minutes, or until a toothpick inserted into the center comes out clean. Allow the cake to cool in the pan for about 10 minutes before transferring it to a wire rack to cool completely.

Enjoy your Plum Crumble Cake warm or at room temperature, perhaps with a dollop of whipped cream or a scoop of vanilla ice cream!