Peel the potatoes and carrots, then coarsely grate them in a food processor or by hand on a box grater. Add a good pinch of sea salt, toss and scrunch it all together, then leave for 5 minutes.
Meanwhile, mix the mustard, a good squeeze of lemon juice, and a couple of lugs of extra virgin olive oil with a little pinch of salt and black pepper in a medium bowl and put aside.
Drizzle a really good lug of olive oil into a large bowl and add a good pinch of pepper. Handful by handful, squeeze the potato and carrot mixture to get rid of the excess salty liquid, then sprinkle into the bowl.
Toss in the oil and pepper until well mixed, then evenly scatter it over a large oiled baking tray (roughly 30cm x 40cm). Roast for around 35 minutes, or until golden on top and super-crispy around the edges.
Meanwhile, blanch the peas for a minute in a large pan of boiling salted water, then scoop out, add to the bowl of dressing and pile the spinach on top.
Just before your rösti is ready, with the water gently simmering, crack in the eggs, poach to your liking, then carefully remove with a slotted spoon.
Serve the rösti with the eggs on top. Quickly toss the salad together to dress it and scatter in piles on the rösti, then crumble over the feta and serve. I like to whack it in the middle of the table and let everyone dig in.
