Preheat oven to 375°F (190°C). Rub squash halves with olive oil and sprinkle with salt.
Place cut-side down on a rimmed baking sheet and roast for 25 minutes, until fork-tender.
Let cool about 10 minutes, then scrape the insides with a fork to pull the strands away from the skin.
In a large skillet, heat 2 1/2 tablespoons olive oil over medium heat.
Add minced garlic and cook for 1 1/2 minutes, until fragrant.
Stir in the spaghetti squash strands, white wine vinegar, minced parsley, minced basil, and 1/4 teaspoon salt.
Cook for about 2 minutes to heat through, stirring gently.
Remove from heat and stir in the shredded Gruyère cheese until melted. Top with toasted pine nuts. Taste and add more salt or black pepper if desired.