Mix basil, flour, milk, 2 eggs, and ½ teaspoon salt into a fairly runny pancake batter.
Heat neutral oil in a large pan over medium-high heat. Fry the pancakes until golden brown. Transfer to a plate and let cool for 2-3 minutes.
In the same pan over medium-high heat, stir-fry the diced chicken breast for 2 minutes. Add the diced tomatoes and mix. Let cook for 1 minute. Season to taste with sugar, salt, and pepper. Add the diced mozzarella, stir, and remove from the heat.
Spread 2 tablespoons of pesto on each pancake. Spread the chicken, tomato, and mozzarella mixture evenly on top. Roll up tightly.
Place the rolled pancakes in an ovenproof dish. Heat in a preheated oven at 180°C (356°F) for 5-10 minutes, until the cheese is melted.