Halve the potatoes. Tip into a large pan, sprinkle generously with salt and cover with around 5cm of cold water. Put the lid on and set over a high heat. Bring to the boil, then simmer for about 15 mins.
While the potatoes cook, chop the broccoli into medium sized florets. Put them in a food processor (see our tip if you don't have one). Zest the lemon and add it with the juice, the mint leaves, 1 tbsp olive oil and some seasoning. Pulse till everything is finely chopped.
Drain the potatoes and put them back into the pan. Crush lightly with a fork or masher. Heat 1 tbsp oil in a large frying pan. Add the potatoes and cook for 5 mins, stirring till the edges are golden and crispy.
Season well. Add the broccoli and toss together, cooking for a further 1 min. Turn the grill on to a medium-high heat.
Rub the salmon fillets with 1 tsp olive oil each. Season. Place skin-side up on a baking tray. Grill for 5-10 mins, or till the skin is crispy and the fish is cooked through and dark pink. Wrap with foil to keep warm while you finish everything.
Fill a pan with boiling water and bring to a gentle simmer. Carefully break in an egg as close to the water’s surface as possible. Repeat with the second egg. Poach for 2-3 mins. Lift out with a slotted spoon.
Spoon the broccoli and potato smash onto each plate. Slide a piece of salmon onto each. Finish with the poached eggs, a scattering of rocket leaves and some cracked black pepper.