Put the squash into the microwave for 1-2 minutes. Remove it and put it on a cutting board. Cut it in half and remove the seeds. Then cut it into small chunks.
In a medium saucepan, add the squash chunks, vegetable broth, soy milk, and garlic. Bring to a boil and then reduce to a low simmer for 20-25 minutes or until the squash is soft. While the sauce is cooking, grate the cheese, set it aside.
Boil the water for the pasta, add salt, and cook the noodles according to package directions.
When the squash is done, carefully pour the mixture into a food processor. Add greek yogurt, salt, and pepper and blend until smooth. Pour the creamy sauce back into the pan and add the cheese. Let it cook until the cheese has melted.
Drain the noodles and put them into the pan with the sauce. Mix well.