Whisk the egg whites with 1 teaspoon water, the dill and pepper in a medium bowl until soft peaks form.
Toss the spinach, tomato and Cheddar in a small bowl.
Lightly coat a small non-stick frying pan with cooking spray and set over moderate heat. When the pan is hot, pour in the egg mixture and cook until it begins to set on the base. Lift up the edge of the setting eggs with a spatula and push the cooked part towards the centre of the pan to let the uncooked egg run underneath. Cook until the omelette is almost set and the base is just lightly browned.
Reserve 1 tablespoon of the spinach filling for garnish, and spoon the rest over half the omelette, leaving a 1cm border. Lift up the omelette at the edge nearest the handle of the pan and fold in half, slightly off-centre, so the filling just peeks out. Cook for a further 2 minutes, then slide the omelette onto a plate. Garnish with the reserved filling and serve at once.