Cook pasta in a large pot of boiling salted water until al dente, about 8 minutes. Drain and rinse under cold water to cool.
In a large bowl, combine the cooked pasta, baby spinach, cherry tomatoes, and red onion.
In a small bowl, whisk together the olive oil, red wine vinegar, minced garlic, oregano, salt, and pepper to create the dressing.
Pour the dressing over the pasta mixture and toss until well coated. Note: If not serving until the next day, store the dressing separately and add before serving.
Sprinkle with grated Parmesan cheese and toss again.
Serve immediately or chill in the refrigerator until ready to serve.