Bring a large pot of lightly salted water to a boil. Cook tortellini in boiling water until al dente, 8 to 10 minutes. Drain and set aside to cool.
Bring a pot of water to a boil and cook peas for 2 minutes. Drain and set aside to cool.
Combine cooled tortellini, cooled peas, tomatoes, Parmesan cheese, chives, and parsley in a bowl.
Combine olive oil, lemon juice, sugar, salt, and pepper in a little bowl; the dressing is supposed to taste sour. Pour over tortellini salad and mix well. Refrigerate at least 2 hours. Taste before serving and season with salt and pepper, if necessary.
