Scrub the potatoes well and then sliced in halves or quarters, depending on the size.
Fill a large saucepan three quarters of the way up with water, add a pinch of salt and bring to a boil. Add the potatoes and cook for 15 minutes, adding the peas and the broccoli florets for the final 5 minutes. Drain the vegetables well and transfer into a large bowl. Add pesto and stir to coat.
Rub the salmon fillets on both sides with olive oil; season with salt and pepper.
Place the salmon in the hot pan, skin-side down, turn the heat down to medium and cook for 4 minutes, or until golden underneath.
Use a slotted spatula to turn them over, then cook the fillets for 2 to 3 more minutes, or until just cooked through.
Remove the pan from the heat, let rest for 30 seconds and sprinkle the salmon with a good squeeze of lemon juice. Serve with the pesto vegetables.