Preheat the oven to 425 degrees. Line a rimmed baking sheet with parchment paper. Add the squash to the baking sheet and toss with olive oil. Bake for 35 minutes. (Keep the oven on and at 425 degrees after removing the squash.)
While the squash is baking, bring a pot of water to a boil. Salt it and cook the zitti according to the length of time on the package. Reserve 1 cup of pasta water before draining.
When the pasta is done, melt the butter in a skillet. Once it is completely melted, whisk in the flour. Once fully combined, very slowly whisk in the reserved pasta water a little at a time to make a roux. This should take no more than a minute.
Whisk the milk, salt, sage, and thyme into the sauce. Bring to a simmer and cook over low heat for five minutes. Remove from the heat.
Add the cooked pasta, cooked squash, turkey, and one cup of cheese to the skillet. Toss gently. Transfer to a 2 quart baking dish that has been sprayed with cooking spray.
Top with the remaining cheese and bake, uncovered, for 10 minutes in the hot oven.