1: Cook the potatoes in boiling salted water for about 10 minutes, until tender. Drain them well and crush lightly, then set aside.
2: Heat the oil and butter in a large non-stick frying pan over a high heat. Add the onion and cook until browned. Add the green pepper and ham and cook for about 10 minutes until the pepper is softened. Remove from the heat.
3: In a bowl, mix together the crushed potatoes, onion, pepper and ham mix, thyme, mustard and cayenne.
4: Sprinkle half the grated Parmesan over the bottom of the frying pan. Place over a medium heat and add the potato mixture, spreading it out in an even layer. Scatter over the remaining Parmesan. Cook, without moving, for 10 minutes or until crispy on the underside.
5: Now turn the potato mixture over. Cook for a further 10 minutes, or until crispy on the other side and hot all the way through. You may want to flip it over again for a few minutes.
6: Meanwhile, poach the eggs in a large shallow pan of simmering salted water for 3–4 minutes. Carefully remove with a slotted spoon, drain on kitchen paper and set aside.
7: Scatter the chopped parsley on top of the hash. Divide between warmed plates and place a poached egg on each portion. Serve the avocado slices and cherry tomatoes alongside.