Toss the squash cubes with the olive oil and salt. Spread out in one layer on a baking sheet and roast until tender, stirring once, 30 to 35 minutes. Remove from the oven. Tip the squash into a bowl and mash until fairly smooth to make about 2 cups of puree.
To the puree, add the flour, shredded Parmesan, egg, baking powder and Italian seasoning, then mix until well incorporated.
Line a baking sheet with parchment paper and lightly coat with cooking spray. Spread the mixture into a 12-inch circle on the baking sheet, spreading into an even layer with the back of a spoon or spatula. Bake until lightly browned, about 30 minutes.
While the pizza cooks, make the pesto: In a food processor, combine the arugula, basil, almonds, grated Parmesan, lemon juice and olive oil, then puree until smooth.
Remove the pizza crust from the oven and carefully slide onto a serving plate or cutting board using a metal spatula (the crust is not super fragile but is more fragile than a regular pizza base).
Top with the pesto and spread it, leaving a 1/2-inch border.
For the toppings: Add the arugula, prosciutto and Parmesan shavings. Drizzle with the balsamic glaze.