Preheat the oven to 200°C/fan180°C/gas 6. Peel and slice the butternut squash into wedges, toss with 1 tbsp olive oil, the unpeeled garlic cloves and the chilli flakes. Season. Roast for 30 minutes.
In simmering water, poach the eggs for 2-3 minutes. Whisk the mustard with the sherry vinegar and 3 tbsp olive oil. Season, then toss with the squash and salad leaves. Scatter over the walnuts. Top with the eggs and Parmesan shavings.