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 small saucepan over medium heat. Whisk in flour; when thoroughly blended, slowly add milk, stirring constantly. Cook until thickened. Stir in cheese.