Place a rack in the center of your oven and preheat to 400 degrees F. Line a large rimmed baking sheet with parchment paper.
In a large bowl, stir together the squash, olive oil, garlic, salt, Italian seasoning, pepper, and half of the Parmesan cheese. Spread into a single layer on the prepared baking sheet. Roast in the oven for 10 minutes.
Remove the pan from the oven and carefully toss the squash. Spread back into an even layer, sprinkle with the remaining Parmesan, then return to the oven and continue cooking until the squash is tender and the Parmesan is golden, about 10 additional minutes. Transfer to a bowl (or serve it right off the baking sheet). Sprinkle the thyme over the top. Enjoy hot.
Make-ahead tip: Squash can be cubed and stored (uncooked) in the refrigerator 1 day ahead.
Store leftovers in the refrigerator for up to 4 days. Reheat gently in the microwave, a nonstick skillet, or in the oven.