Preheat oven to 190C and line a baking tray with baking paper. Combine pumpkin, potato, onion and thyme in a large bowl and season to taste.
Heat 40ml oil in a frying pan over medium-high heat, add a quarter of the pumpkin mixture, press down to 1cm thick and cook, turning once, until golden brown (2-3 minutes each side). Transfer to prepared tray and place in oven until cooked through (5 minutes). Repeat three times with remaining pumpkin mixture.
Poach eggs in a saucepan of simmering water until soft-poached (3 minutes).
Combine salad ingredients in a bowl, season to taste and serve with rösti topped with a poached egg and lemon wedges.