To make the pesto, place the basil and pine nuts in a food processor and blitz until broken down. Add the cheese and garlic and blitz briefly. With the motor still running, slowly pour in the oil through the feed tube until combined.
Cook the broccoli and sugar snap peas in a large saucepan of boiling water for 7–8 minutes until 'al dente'.
Meanwhile, bring a saucepan of water to a gentle simmer and stir with a large spoon to create a swirl. Break 2 of the eggs into the water and cook for 3 minutes. Remove with a slotted spoon and keep warm. Repeat with the remaining eggs.
Drain the vegetables, then return to the pan and add 1 1/2 tablespoons of the pesto (store any remaining pesto in an airtight container in the refrigerator) and the sun-dried tomatoes. Gently toss together until well coated.
Serve topped with the poached eggs and Parmesan shavings and sprinkled with pepper.