Microwave whole squash on High 5 minutes to soften. When just cool enough to handle, cut lengthwise in half and scoop out seeds. Place, cut side down, in a shallow microwave-safe dish and microwave on High until flesh is completely softened, about 8 to 10 minutes. Let stand until cool enough to handle, about 15 minutes. Using a fork, pull squash from skin in long strands; set aside.

While squash is cooling, heat 1 tablespoon oil in a large nonstick skillet over medium-high heat. Add meatballs and turn to coat. Reduce heat to medium and cook, turning occasionally, until browned and cooked through, about 15 minutes. Transfer meatballs to a saucepan and add sauce (reserve skillet); cook over medium-low heat until heated through, about 2 minutes.

Wipe skillet clean, add remaining 1 tablespoon oil and heat over medium heat. Add garlic and cook 1 minute. Toss in squash and saute 2 minutes; salt and pepper to taste.

On a serving platter, mound squash, top with meatballs and sauce, then sprinkle with parsley and cheese.