Filling: Heat the oil in an ovenproof casserole dish. Add the onion then cook and stir until soft. Add the mince and carrots, then cook until the meat is no longer pink. Add the flour and stir well. Add the peas, mushrooms, water, stock, herbs, salt and pepper. Stir well and simmer for 10 minutes.
Cobbler: Place the flour, suet and herbs in a dish, then season and stir well. Add the water, a little at a time, and mix, adding just enough to make a soft ball. Lightly flour a work surface and turn the mixture out. Cut into eight pieces and form each into a ball.
To Assemble: Gently place the cobbler balls on top of the meat mixture and brush the top with beaten egg or milk, to help it brown.
Bake in the oven for 25 to 30 minutes, or until the dumplings are browned. Remove from the oven and serve hot.