Combine milk and butter in a medium saucepan; bring to a boil. Add flour all at once, stirring vigorously; cook over medium heat, stirring constantly, until mixture leaves sides of pan and forms a smooth ball. Remove from heat, and cool slightly.
Add eggs, one at a time, beating well after each addition; beat until batter is smooth. Drop batter by teaspoonfuls into simmering soup or stew. Reduce heat; cook, uncovered, 10 minutes.