Prep: 7 minutes; Cook: 12 minutes. Cut the cream cheese while chilled, and let stand at room temperature about 15 minutes before using.
In a medium bowl, using a stick blender or whisk, beat the eggs until completely combined. Add the salt and pepper.
In a nonstick medium skillet, heat the butter over medium heat just until very hot. Add the eggs and reduce heat to medium-low. Cook until set around the edges. Using a heatproof rubber spatula, fold the eggs over on themselves. Repeat folding. Continue cooking until the eggs are set into soft, moist curds, about 10 minutes.
Reduce heat to low. Add cream cheese and salmon to eggs and fold until cream cheese is incorporated, about 2 minutes. Remove from heat.
Serve a scoop of eggs (about 1/2 cup) over 1/2 slice of toast. Sprinkle with chopped chives.