Cut your broccoli up to make 'trees', but not too small. It's best, I have found, to leave as much of the stalk as possible to be used as a handle, but if you think that it makes the 'tree' part too big then slice up through the stalk to half or even quarter it lengthways.
Steam your broccoli over some boiling water for 6-7 minutes then leave to cool (or run under cold water if you are in a hurry, but remember that if you feel it's too hard still that this will stop the cooking process).
Give it to your child and if they are good and clever they will hold it by the 'handle' and eat the 'tree'. My child resolutely refuses to do anything but dig her fingers into the branches of the tree part and chew on the stalk, which causes the top part to disintegrate in the most alarming fashion and to fly across the room. It goes EVERYWHERE. You know those chubby little folds of fat that you love to tickle? In there. And that beautiful, expensive high chair* you bought? In every seam of the the fabric seat, every hinge, every corner. Broccoli, my friends, is very much a pre-bathtime vegetable. But delicious and healthy and oh-so enjoyable for the babies.
*Please see Top Tips on buying a highchair.