Bring a large saucepan of generously salted water to a boil. Add both peas and boil until just tender, about 1 1/2 minutes. Using a slotted spoon, transfer the peas to a colander set over a bowl. Rinse the peas briefly under cold water to cool. Drain well.
Add the pasta to the boiling water and cook until tender but still firm to the bite, about 10 minutes. Drain the pasta (but do not rinse) and transfer it to a large bowl.
Add 2 tablespoons of olive oil, 1 tablespoon of vinegar, and the garlic to the hot pasta and stir to combine. Let the pasta stand until it cools to room temperature.
Add the peas, green onions, parsley and ricotta salata to the pasta. Add the remaining 2 tablespoons of olive oil and 2 tablespoons vinegar. Season the salad to taste with salt and pepper and mix well. Serve at room temperature.