Pour enough water into the saucepan to cover eggs by at least 1 inch (2.5 cm).
Bring water to a boil over high heat. Immediately remove pan from heat to stop boiling. Cover saucepan and let eggs stand in water for 2 to 4 minutes until cooked as desired.
Drain water; immediately run cold water over eggs to cool them a little.
Place eggs in egg cups.
Toast bread; spread with butter.
Cut toast into 1-inch (2.5 cm) strips.
Crack tops off eggs with knife.
Serve toast strips with eggs for dipping into soft yolks.