MELT butter in a medium non-stick frying pan over medium. Add corn kernels and cook until heated through, 2 min. Beat eggs with salt. Season with fresh pepper. Stir in tomato and basil. Add to pan.
COOK without stirring until edges set, 2 to 3 min. Lift edge of omelette with a spatula, pulling toward the centre and tilting pan to allow uncooked eggs to run underneath. Sprinkle with cheddar. Flip and slide omelette onto plate.