Heat the olive oil in a non-stick skillet over medium heat.
Add the prosciutto slices to the skillet and cook until golden and crispy, about 2 minutes per side. Remove and set aside on a paper towel to drain.
In a medium bowl, whisk together the eggs, Greek yogurt, lemon zest, sea salt, and black pepper until the mixture is smooth and well-combined.
In the same skillet used for the prosciutto, add the baby spinach and sauté for 1 minute until just wilted.
Reduce the heat to low and pour the egg mixture over the spinach.
Using a silicone spatula, gently stir the eggs, pushing them from the edges toward the center to create soft, creamy curds.
Once the eggs are just set but still moist, remove from heat immediately.
Transfer the eggs to a plate, crumble the crispy prosciutto over the top, and garnish with finely chopped fresh chives.