Combine 1 cup flour, corn starch, sugar, undissolved yeast and salt in large mixer bowl with whip attachment in place. Heat milk and 1/4 cup butter until very warm (120°F to 130°F). Add to flour mixture. Beat 2 minutes at medium speed of electric mixer, scraping bowl occasionally. Add egg and 1 cup flour; beat 2 minutes at high speed. Switch to dough hook attachment. Stir in enough remaining flour to make a soft dough. Continue mixing on low speed for 6 to 8 minutes or hand knead on lightly floured surface until smooth and elastic, about 8 to 10 minutes. Cover; let rest 10 minutes.
Roll dough on lightly floured surface to a 16 x 12-inch rectangle. Use a cheese grater to shred 5 tablespoons of cold butter onto center third of dough; fold ends over butter, pressing edges to seal butter in. Turn dough one quarter turn. Repeat rolling, arranging butter, folding and turning procedure twice more. Cover with plastic wrap; refrigerate for 2 hours. (Dough may be held overnight in refrigerator or frozen.)
Divide dough in half. On lightly floured surface roll each half to a 16-inch circle. Cut each into 8 pie-shaped wedges. Roll up each wedge beginning at wide end. Place, points down on 2 nonstick baking sheets. Curve ends to form crescents. Prepare EGG GLAZE by beating egg with 1 teaspoon water. Brush croissants with EGG GLAZE. Cover; let rise in warm, draft-free place until doubled in size, about 1 hour.
Preheat oven to 425°F and bake for 12 to 15 minutes until deep golden brown on top. Remove from sheets with a spatula; serve warm.