Place 1 tablespoon tomato puree in four 6-ounce custard cups. Place one poached egg on top of puree in each cup. Set cups aside.
Melt butter in a small saucepan over low heat; add flour, stirring until smooth. Cook 1 minute, stirring constantly. Gradually add milk; cook over medium heat, stirring constantly, until thickened and bubbly.
Spoon equal amounts of white sauce over eggs in custard cups. Sprinkle cheese over top of white sauce; add salt and pepper. Bake at 350° for 5 minutes or until cheese melts. Serve immediately.