Squeeze spinach to remove any excess water. Blend eggs with a fork in a medium bowl. Add cheese, spring onions, dill, pepper and the spinach; mix gently with a rubber spatula.
Set a rack about 4 inches from the heat source; preheat the grill.
Heat oil in a 10-inch non stick frying pan over medium heat. Pour in the egg mixture and tilt to distribute evenly. Reduce the heat to medium-low and cook until the bottom is light golden, lifting the edges to allow uncooked egg to flow underneath, 3 to 4 minutes. Place the pan under the grill and cook until the top is set, 1 1/2 to 2 1/2 minutes. Slide the omelette onto a platter and cut into wedges.