Gather the ingredients.

Place eggs in a saucepan and cover with cold water. Bring water to a boil and immediately remove from heat. Cover and let eggs stand in hot water for 10 to 12 minutes. Remove from hot water, cool, peel and chop.

Melt butter in a saucepan over medium heat; stir in flour until smooth. Gradually mix in milk so that no lumps form and stir constantly until mixture comes to a boil.

Stir white pepper, salt, black pepper, and chopped eggs into the sauce; stir until eggs are heated through.