Heat the oven to 350°F.
Melt 1 tablespoon of the butter in a medium frying pan over medium heat. Increase the heat to high, add the shrimp, and sauté until they’re about three-quarters of the way done—crisp-tender and still translucent in the center.
Add the tomatoes and spinach and sauté for 1 minute or until the spinach is completely wilted. Remove from heat and add the chives. Season generously with several pinches of salt and pepper.
Place a 6-inch ovenproof nonstick skillet or well-seasoned cast iron pan over medium heat. Add the remaining 3 tablespoons butter and swirl it in the pan to coat evenly. Add the egg whites and spoon the shrimp mixture into the center. Bake in the oven until the eggs are puffed and completely set in the center, about 10 to 12 minutes.