Prepare the pasta according to the package directions. Drain, rinse with cold water and allow to cool.
In a large skillet, heat 1 Tablespoon olive oil on medium.
Add onions and squash and saute for 3 minute.
Add mushrooms and garlic and saute for 2-3 minutes more, until vegetables are just cooked, but not wilted.
Remove vegetables from the heat and allow them to cool for a few minutes.
Combine the vegetables and pasta in a large bowl and toss with remaining 3 Tablespoons of olive oil and feta cheese. Season with salt and pepper, to taste.
Serve immediately or refrigerate for several hours and serve cold. Garnish with basil and additional feta cheese.