Preheat the oven to 400°F. If using a stone/steel, put it on a rack in the center or bottom third of the oven before you start preheating.
Place the cubed butternut squash on a foil or parchment-lined baking sheet, drizzle with a little olive oil, and season with salt and pepper. Transfer the baking sheet to the oven and roast the squash for 25 minutes or until it’s tender and just beginning to caramelize. Remove the squash from the oven and set it aside to cool.
Increase the oven temperature to 500°F (if using a baking sheet) or as hot as your oven can get (if using a baking stone or steel).
In a large bowl, toss together the spinach and the roasted squash.
Stretch or roll out your dough to a 12- to 14-inch circle, then transfer it to an oiled or parchment-lined baking sheet or a lightly floured pizza peel (if using a baking stone/steel).
Transfer the spinach-squash mixture to the dough, then top with the cheese and drizzle on the cream.
Transfer the pizza to the oven and bake just until the crust turns golden and the cheese melts, about 5 minutes on a baking sheet or about 3 minutes on the baking stone/steel. While the pizza bakes, crack the eggs (if using) into separate small ramekins or bowls.
Carefully pull out the oven rack. Slide the eggs (if using) onto the pizza, trying your best to place one in each quadrant of the pizza. Bake the pizza for another 3 to 5 minutes, until the egg whites are set but the yolks are still jiggly.
Remove the pizza from the oven and let it rest for 5 minutes, then slice and serve.