Preheat oven to 375°F. Line a baking sheet with parchment paper.

Cut spaghetti squash in half lengthwise, and scoop out seeds, leaving the flesh intact.

Drizzle cut side with 2 tablespoons evoo, and season with salt and pepper. Place cut-side down on prepared baking sheet. Roast in a 375°F oven for 30 to 40 minutes, or until a knife can be inserted with no resistance.

Meanwhile, toss tomatoes with 2 tablespoons evoo, salt, and pepper. In the last 15 minutes of cooking, place tomatoes in the oven along with the squash for 15 minutes, or until blistered.

Remove squash and tomatoes from oven and cool. With a fork, gently scrape the fragile squash strands into a mixing bowl. 

Heat 2 teaspoons of evoo in a large saute pan. Add anchovies and cook for 3 to 5 minutes, until anchovies melt into hot oil. Add garlic, olives, capers, and spaghetti squash. Gently toss together.

Fold in roasted tomatoes, parsley, and 1 tablespoon of evoo. Sprinkle Parmesan cheese on top (if using). Serve immediately.