Cut spaghetti squash in half lengthwise. Using a spoon, scoop out inner flesh and seeds.
Drizzle 1 tablespoon of olive oil on spaghetti squash and place face down on a baking sheet. Bake in preheated oven for 45 minutes, until a fork can easily pierce through the skin.
While spaghetti squash is in the oven, add tomatoes to a baking dish. Drizzle remaining 1/2 cup olive oil over tomatoes and add garlic, salt and pepper. Move tomatoes to the edges of the dish and place the block of feta in the center.
Bake in the preheated oven for 35 minutes, until tomatoes burst and feta is nearly melted. Once done, turn oven to broil and broil for an additional 5 minutes.
While tomatoes and feta are in the oven, cook and drain the pasta.
Remove tomatoes and feta from the oven and mix well. Scrape strands from the spaghetti squash and add 1/2 of the squash to the baking dish. Add the pasta and mix well to combine. Garnish with fresh chopped basil.
Serve immediately or store in an airtight container for 3-4 days.