Preheat oven to 425°F/ 225°C.
Cut the squash lengthwise into wedges, then place them cut-side down on a rimmed baking sheet. Drizzle with 4 tablespoons olive oil and season with salt and pepper.
Roast, without turning, until completely tender and caramelized, about 45 minutes. Broil for 5 minutes or until the top browns and caramelizes. If making ahead, reheat in the oven closer to serving, at 425° for 10-15 minutes.
Meanwhile, melt the butter in a small saucepan or skillet over medium heat. Once it starts to foam but before it’s brown, add the remaining 2 tablespoons olive oil and walnuts. The nuts will foam up and disappear into the butter - don’t forget about them.
Swirl the pot, stirring constantly and continue to cook the walnuts in the browning butter. Eventually, the walnuts will toast and the butter will brown, 4-6 minutes.
Remove from heat, add the dates and season with salt and pepper. If making ahead, rewarm the mixture gently over medium heat right before serving.
To serve, transfer squash to a large serving platter or shallow bowl. Spoon walnut/date mixture over and scatter with parsley, flaky salt and another good grind of black pepper.