Pre-heat oven to 400ºF.
Season cut side of pumpkin or squash with 1 tablespoon EVOO, salt and pepper. Place cut-side down onto a baking sheet and drizzle with another tablespoon EVOO. Transfer to the oven and roast until tender, 45-50 minutes and let cool.
While the squash is roasting, place a medium skillet over medium-high heat with 2 turns of the pan of EVOO, about 2 tablespoons. Sauté chorizo until golden brown and crispy, 6-7 minutes. Remove to a paper towel-lined plate and cool.
When cool enough to handle, scoop the pumpkin or squash flesh out of the skin and puree it in a food processor. Turn the puree out into a medium-size mixing bowl and combine it with the chorizo, thyme leaves, hot sauce, paprika, and cinnamon. Season lightly with salt and pepper and reserve.
Lightly dust a work surface with flour and lay out one pie crust. Roll it out slightly so it’s the thickness of a nickel. Cut into eight evenly sized triangles, just like you’d cut a pie. Transfer triangles to a baking sheet and repeat the rolling and cutting with the remaining pie crust. You should have 16 bottoms on a baking sheet and 16 tops when you’re all done.
Divide the filling among the triangles on the baking sheet leaving a little room at the edges to seal the pockets. Brush the edges of each triangle with egg wash then top each triangle with the remaining wedges of dough, pressing lightly around the perimeter to seal the filling inside. If you like, take a fork and lightly press the very ends of the tines into the border of each pocket to give it a fancy finish.
Lightly brush each turnover with egg wash. Bake until crust is deep golden brown and crisp, about 20 minutes. Serve with Sherry-Shallot Warm Brussels Sprouts Slaw alongside.