Preheat the oven to 400 degrees F (200 degrees C). Grease a baking sheet.

Place squash skin-side down on prepared baking sheet: bake until cooked through, about 1 hour. Cool for 10 minutes. Scrape flesh into string-like strands with a fork: place in a bowl.

Melt 1 tablespoon of butter in a large skillet over medium-high heat: add onion. Cook and stir until onion begins to turn translucent. Stir in mushrooms and kale; reduce heat to medium-low.

Stir in squash, remaining 2 tablespoons butter, garlic salt, Italian seasoning, and red pepper flakes; cook for 2 minutes. Transfer squash mixture to a large bowl.

Stir pesto and olive oil into squash mixture. Slowly stir in grated Parmesan cheese until evenly mixed.