Heat your oven to 180°C/Fan 170°C/Gas 4. Line a baking tray with baking paper.
Scrub the sweet and normal potatoes. Coarsely grate them. Place into a large bowl.
Coarsley grate the cheddar and add to the potatoes. Add 2 tsp caraway seeds and plenty of salt and pepper. Beat 1 egg. Pour into the potatoes with 1 tbsp olive oil. Mix everything together really well.
Dollop 6 spoonfuls onto the baking tray. Lightly press down on the mounds with your hands to squish them together. Slide the tray into the oven and cook for 25-30 mins. They should be crisp on the outside and cooked through in the middle.
While the hash browns cook, halve the chilli. Flick out the seeds and finely chop it. Finely chop the mint leaves. Peel and grate the garlic. Zest and juice the lemon into a bowl. Add the chilli, mint and garlic. Whisk with 1 tbsp olive oil. Add a pinch of salt and pepper. This is your dressing.
Halve the avocado and scoop out the flesh. Thinly slice it. Toss with a little of the chilli dressing to stop it going brown.
When the hash browns have 5 mins left to cook, fill a small pan with boiling water. Crack an egg into a small dish. Carefully lower it into the pan of gently boiling water. Repeat with the other eggs. Cook on a gentle bubble for 2 mins for a runny yolk or 3 mins for a slightly more well-cooked yolk. Lift out of the pan with a slotted spoon and place on a plate lined with kitchen paper. You may need to do this in batches of 2 eggs at a time.
Arrange the rocket on two plates. Top with the hash browns, a few slices of avocado and a couple of eggs each. Drizzle over the zingy mint dressing to serve.