Heat 2 Tbsp olive oil in a large skillet over medium-high heat until shimmering, then add the meatballs in a couple of separate batches (being careful not to crowd the pan) and brown them for about five minutes, turning occasionally.
Remove browned meatballs from the skillet to a large plate (they will not be cooked all the way through, but will finish cooking in the soup).
Stir in spinach, reduce heat to medium-low, and continue simmering for another couple of minutes, just until spinach is wilted.
Taste and season with sea salt and pepper to taste. Serve your Italian wedding soup garnished with additional grated Parmesan, to taste.
You can make the meatballs even smaller, if you like, but might reduce the browning time a bit if you choose to do so.