Cook the carrots in lightly salted boiling water for about 8 minutes until only just tender. Drain thoroughly and leave to cool. Process in a food processor until finely chopped.
Heat the oil in a frying pan on the hob and gently fry the onion for 2–3 minutes to soften. Tip into a bowl, add the carrots, Cheddar cheese, breadcrumbs, herbs, a little salt and plenty of pepper. Stir well to mix. Add the egg and yolk, and mix to a dough that holds together.
Turn out on to a lightly floured surface and divide into 12 even-sized portions. Shape each into a sausage and arrange on a lightly oiled baking sheet, spacing them slightly apart. Cover loosely and chill for 30 minutes. Place the baking sheet on the upper rack of the halogen oven.
Set the temperature to 225°C (437°F) and cook for 12–15 minutes, turning the sausages once they are golden on the surface and watching closely to check that they do not brown too much. Serve with fried mushrooms and baked beans.