In a large bowl, beat the butter, brown sugar and granulated sugar together until light and fluffy.
Add the eggs one at a time, beating well after each addition.
Stir in the vanilla.
Add the baking powder, salt, cinnamon, ginger, cloves and nutmeg, and beat to combine.
Add the buttermilk and stir again. The mixture will look curdled and rather thin.
Add the flour and mix until just combined.
Arrange several pieces of cooked rhubarb into the bottom of each cupcake tin. Spoon a little of the juice from the cooked rhubarb into each tin as well (it's okay for it to be quite wet).
Drop a large spoonful of cake batter into each cupcake tin on top of the rhubarb. You can spread it around a little bit with a spoon to flatten it out, but it doesn't have to be perfect. It will spread itself while it bakes.
Bake mini cakes for 12-15 minutes, or until a toothpick inserted into the centre comes out clean.
Allow the cakes to cool in the pan for just a couple of minutes, before flipping them onto a wire rack to cool. (Don't let the cakes cool down too long, you want to flip them while they're still hot so they don't stick).