Soak the red onion slices in cold lightly salted water until ready to use – this will help remove the bitterness.
Mix the balsamic vinegar with the olive oil and salt. The easiest way to do this is to put them in an airtight container and shake them until the ingredients are blended.
Strain the onions and mix them with the arugula and the balsamic olive oil dressing.
Layer the strawberry slices, goat cheese and spicy pecans on top.
Toss table-side and serve immediately.
Whisk the olive oil, lemon juice, salt, and a few grinds of black pepper together in a large bowl. Add the arugula and toss to combine. Top with the shaved Parmesan and serve immediately.
Make ahead: The dressing can be made up to 5 days ahead of time and stored in an airtight container in the refrigerator. Rewhisk again before using.