If your new potatoes are very small, leave them whole. If not, halve or quarter them. Cut stem off broccoli, remove the tough outer fiber, and chop inner stem coarsely. Also chop the broccoli head.
Steam, over boiling water, the potatoes, broccoli stem, carrots and cauliflower. After 10 minutes, add broccoli. Continue to stem another few minutes until vegetables are just tender when pierced with a fork.
Meanwhile, in a large, heavy skillet or stew pot, saute the onions in half the niter kebbeh until they are parent. Mix in the steamed vegetables, except broccoli. Cover and cook for 6-8 minutes , stirring frequently. Add broccoli. and cook for another 4 or 5 minutes. Heat the remaining niter kebbeh to pass around at the table. Serve yataklete kilkil with injera.