For the pretzels, in a large bowl, whisk together the warm water and yeast until the yeast has dissolved. Stir in 500g/1lb 1½oz of the flour (the mixture should form quite a loose batter). Cover with cling film or a damp tea towel and set aside in a warm place for a few hours, or until the batter has almost doubled in size and the surface is covered with air bubbles.
Place the remaining flour into the bowl of an electric stand mixer. Add the salt and sugar, then add the olive oil and tip in the risen pretzel batter. Using the dough hook attachment, work the mixture for 6-7 minutes over a slow speed, until it comes together to form a smooth dough that comes away cleanly from the sides of the bowl. Turn the dough out onto a floured work surface. (Alternatively, if you do not have a stand mixer, knead the ingredients together on a floured work surface until smooth and elastic.)
Roll the dough out into a sausage shape about 2cm/1in thick. Form the dough into a large pretzel shape and pinch the ends together to secure. Place onto a greased baking tray. Cover and set aside to rise in a warm place for 30 minutes or so.
Preheat the oven to 220C/430F/Gas 7.
To finish the pretzel, mix the beaten egg with the water and brush the mixture over each pretzel. Sprinkle the pretzel with your preferred topping of salt flakes, poppy seeds or sesame seeds.
Bake the pretzel in the oven for 30 minutes, or until golden-brown and cooked through.
For the corned beef hash, melt the butter in a frying pan until foaming and gently fry the onion for 2-3 minutes, or until softened.
Add the potatoes and the corned beef and fry for 5-6 minutes, pressing down the mixture every so often with a fish slice, until the mixture is golden-brown and crisp.
When the corned beef hash is cooked, remove the pan from the heat, sprinkle over the Worcestershire sauce and parsley and season to taste with sea salt and freshly ground black pepper.
For the poached eggs, pour enough water into a large deep pan so that it is two-thirds full. Bring to the boil.
Place the eggs, still in their shells, into the boiling water for 20 seconds, then remove with a slotted spoon.
Add a splash of white wine vinegar to the pan, then swirl the water gently to create a whirlpool effect. Crack one egg into the centre of the whirlpool and poach for 2-3 minutes, or until the egg is cooked to your liking. Remove from the pan with a slotted spoon and set aside to drain on kitchen paper. Keep warm. Repeat the process with the remaining eggs.
To serve, spoon the corned beef hash onto four serving plates and top each with a poached egg. Break the large pretzel into four pieces to serve.