Preheat the olive oil in a large nonstick skillet over medium high heat. Add in the celeriac and cook for 3 minutes, until you start to see some colour develop. Add in the sunchokes and cook for another 5 minutes, stirring every once in a while. Add in the celery, cauliflower and rosemary, and continue to pan-fry for another 2 minutes.

Add in the water, cover and cook on medium low until the vegetables are nearly completely tender, about an additional 5 minutes.

Remove the lid, and add in the pear, maple mustard, and lemon juice. Season with salt and pepper and cook on low heat until everything is mixed throughout and warmed through. Sprinkle with the grated cheddar cheese and keep warm on low heat.

Meanwhile, heat a large nonstick skillet with a teaspoon of oil over medium heat. Add in the eggs (or do in batches), sprinkling the yolks with a bit of salt and pepper, cooking until the whites are set.

Divide the hash between four plates and top with a fried egg.