Warm milk to 100-110°F. Sprinkle yeast and 1 teaspoon sugar over milk, stir once, and let sit for 5 minutes until foamy.
2.25 tsp active dry yeast, 0.75 cup whole milk, 0.25 cup granulated sugar
Mix flour, remaining sugar, salt, and cinnamon in a large bowl. Pour in proofed yeast mixture and vanilla extract. Stir until a shaggy dough forms, then knead on floured surface for 5-6 minutes until smooth and slightly tacky. Cover with plastic wrap and let rise at room temperature for 1 hour until doubled.
3 cups all-purpose flour, 0.25 cup granulated sugar, 1 tsp salt, 1 tsp ground cinnamon, 1 tsp vanilla extract, 2.25 tsp active dry yeast, 0.75 cup whole milk
Roll dough into a 12x8-inch rectangle. Flatten cold butter between parchment to an 8x4-inch block. Place butter on bottom half of dough, fold dough over butter to enclose. Roll gently to 16x8 inches, fold into thirds like a letter. Wrap and chill 30 minutes. Repeat rolling, folding, and chilling two more times.
1 cup unsalted butter
Roll laminated dough into ⅛-inch thick rectangle. Cut into triangles with 3-4 inch bases. Roll each triangle tightly from wide end to point, curve ends inward to form horns. Place croissants 2 inches apart on parchment-lined sheet. Cover loosely and proof at 75-80°F for 1.5-2 hours until doubled and jiggly.
Preheat oven to 350°F. Beat egg with 1 tablespoon water. Brush croissants gently with egg wash 5 minutes before baking. Bake for 15-20 minutes until deep golden and crisp. Cool on wire rack 15 minutes before serving.
1 large egg
