Lightly whisk eggs and milk in a small bowl and season to taste.
Melt half the butter in a frying pan over medium heat, add spinach and toss constantly until wilted. Remove and keep warm.
Turn heat to medium-low, wipe out the frying pan, add remaining butter and cook until foamy. Pour in egg mixture. Using spatula, slowly push eggs across the frying pan in one motion, wait a few seconds before pushing in the opposite direction. Continue to push and fold eggs until almost set. Remove from heat and fold in the cheese.
Serve immediately on toasted muffins topped with spinach. Sprinkle with chives, extra cheese and pepper.