Heat olive oil in small skillet over medium-low heat. Pour in enough or beaten egg to coat the bottom of the pan and cook until edges start to round, 1-2 minutes. Flip the egg and cook until edges are slightly golden and egg is cooked through, 20-30 seconds. Transfer to plate and repeat with remaining egg.
To serve, spread 2 tbsp of pesto onto each egg pizza. Top with shredded chicken and sun-dried tomatoes. Garnish with pine nuts.