Bring a pan of water to the boil, add the pasta and cook for 10-12 minutes. Drain, reserving 150ml of the cooking water, then stir the spinach leaves into the warm pasta and leave to wilt.
Meanwhile, heat a large non-stick pan over a medium heat, add the bacon and cook for 5 minutes, turning occasionally, until crisp. Remove to kitchen paper, let cool slightly then break into pieces.
Meanwhile, in a food processor whizz the petits pois with the mint, pine nuts, garlic, Parmigiano, reserved pasta water and vegetable oil. Set aside in a small bowl.
Bring another pan of water to the boil. Add the vinegar, then carefully crack in the 4 eggs, one at a time. Cook over a gentle heat for 2 minutes until set but still soft in the middle. Remove carefully with a slotted spoon and drain on kitchen paper.
Mix the pasta and spinach with the pea and mint pesto. Divide among 4 bowls, then scatter over the bacon pieces and place a poached egg on the top.