Place spaghetti squash, cut-side down, on parchment paper-lined baking sheet. Bake in 400 degrees Fahrenheit (200 degrees Fahrenheit) oven until flesh is tender, about 50 minutes. Let cool for 15 minutes.
Using fork, separate flesh into strands into bowl to make about five cups squash. Sprinkle with most of the cheese and all of the parsley, salt and pepper; toss gently with two forks to mix. Transfer to serving bowl and keep warm.
In heavy bottomed skillet, melt butter over medium heat. Add sage leaves to pan and increase heat to medium-high. Cook, stirring gently, until darkened and curled up, two to three minutes. Remove with slotted spoon to plate.
Add garlic to pan; cook until fragrant, about 30 seconds. Stir in vinegar. Drizzle over squash in bowl. Sprinkle with remaining cheese and reserved sage leaves.