Prepare pasta according to package instructions. (Make sure and add 2 tablespoons salt to the pasta water). Remove pasta to a rimmed baking sheet to cool. Don't discard the cooking water.
Add carrots and squash to the boiling water and cook for 1 minute. Remove carrots and squash to a large mixing bowl and cool. Add cooled pasta to the mixing bowl.
Add the cucumber, tomatoes, cheese, green onions, parsley and lemon zest. Stir to combine.
Refrigerate salad covered with plastic wrap. Prepare Creamy Vinaigrette and refrigerate.
15 minutes before serving, pour over Creamy Vinaigrette over the pasta salad and gently stir to combine.
Prepare Creamy Vinaigrette: Add lemon juice and mayonnaise into a 2-cup measuring cup. With a small whisk, stir in garlic, Italian seasoning, salt, and pepper. Slowly whisk oils into mixture to make an emulsified vinaigrette.