Beat cream cheese at medium speed until smooth. Add 2 eggs; beat until smooth. Add remaining 3 eggs, milk, pepper, and salt; beat until blended. Stir in green onions.
Melt butter in large nonstick skillet. Add egg mixture; cook over medium-low heat, without stirring, until egg mixture begins to set on bottom. Draw a rubber spatula across bottom of skill to form large curds.
Add shredded cheese and bacon. Continue cooking until cheese melts and eggs are firm but still moist (do not stir constantly). Serve immediately.