Mix flour, sugar, yeast, and salt. Add milk to form dough.
Knead until smooth; chill 30 minutes.
Pound butter into flat sheet; encase in dough.
Roll and fold dough 4 times, chilling between turns.
Roll into rectangle; cut triangles; shape croissants.
Proof until puffy and jiggly (1.5–2 hours).
Brush with egg wash, bake at 375°F for 20–25 minutes.
Mix filling ingredients; pipe into cooled croissants.
Drizzle lemon glaze over top and serve.