Preheat oven to 180°C fan-forced. Grease a 12-hole (1/2 cup-capacity) muffin pan.
Drop 12 Broccolini® into a saucepan of boiling salted water. Cook for 2 minutes, until bright green and just tender. Drain well and pat dry with paper towel. Cut them in half crossways, set the flower ends aside. Finely chop 4-6 stems, you need 1/4 cup, set the rest aside (see tip).
Combine the flour, sugar, carrot, zucchini, shallots, ham, cheese and chopped Broccolini® stems in a large bowl. Whisk eggs, oil and milk together, season with salt and pepper. Add to ham mixture, stir gently to combine. Divide evenly among muffin holes. Bake for 20-22 minutes or until light golden and cooked through. Stand in pan for 5 minutes, then transfer to a wire rack.
Carefully make a hole in the centre of each muffin using end of wooden spoon. Insert the Broccolini® and sprinkle with extra cheese. Serve.