Melt butter in 8-inch nonstick skillet until sizzling. Meanwhile, toast bagel in toaster.

Leaving yolks intact gently break eggs into skillet. Cook over low heat until egg whites are completely set and yolks begin to thicken but are not hard. Sprinkle with salt and pepper.

Lightly spread cream cheese over one half of the bagel, add tomatoes, arugula, and top with egg.