Preheat the oven to Gas Mark 6, 200C (400F).
Peel the squash and cut into 2-3cm cubes. Place the squash cubes in a large bowl. Drizzle with a tablespoon of the olive oil, then sprinkle over the chilli flakes and season with salt and pepper. Mix well.
Spread the cubes in a single layer on a roasting tin, taking care that they do not overlap. Roast for 20-25 minutes until tender.
To cook the broccoli: Bring a sauce pan of water to the boil. Add a pinch of salt then add the broccoli. Bring the water back to the boil, then drain the broccoli.
To make the dressing: Whisk together the mustard, vinegar and olive oil with a pinch of salt and pepper. Set aside.
To cook the bacon: Heat a non-stick frying pan over a medium-high heat and add a drop of olive oil. Add the bacon lardons and fry for 5-7 minutes, stirring occasionally, until crisp. Remove to a plate and keep warm.
Add the broccoli into the pan and stir fry for a couple of minutes.
To poach the eggs: Bring a large pan of water to the boil. Add the vinegar and season with salt and keep at a very gentle simmer. Break two of the eggs into the water and simmer for 3-4 minutes until just cooked but still soft on the inside. Remove with a slotted spoon and drain well on kitchen paper. Repeat with the remaining eggs.
Divide the butternut squash between 4 plates, then add the broccoli and bacon. Drizzle over the dressing and top with eggs. Scatter over some cheese shavings and serve.