Grease a 9 x 9 inch (23 x 23 cm) cake tin. Set aside.
Get a large bowl of water, put a few drops of lemon juice in it (you are going to use this to stop your pears from browning on you.)
Peel, core and chop the pears into chunks. Drop the chunks as you go along into the water.
In a frying pan, melt the butter, cinnamon and sugar over medium heat. While this is happening, drain the pears in a colander, then place on paper towel (we're going to get some water off them so they don't splatter at you in the next step.)
Fry the pear chunks in the melted butter and sugar until the chunks are tender -- don't cook until the sugar sauce darkens. Remove from heat, set aside.
Start heating your oven to 160 C / 325 F / Gas Mark 3.
In a bowl, beat butter and white sugar until light and creamy. In another bowl, sift the flour and the baking powder, and in another bowl, beat the eggs.
Now it all comes together. Add the flour and the egg alternately to the butter, starting with the egg. When you are done, use a spatula to spoon in the pears and all of the sauce from the frying pan.
Transfer to the cake tin, and bake until golden and a toothpick comes out clean (about 50 minutes.)