Warm milk to 100-110°F, stir in yeast and 1 teaspoon sugar, let sit 5-10 minutes until foamy. If no foam forms, restart with fresh yeast.
0.75 cup milk, 2.25 tsp active dry yeast, 0.25 cup granulated sugar
Mix flour, remaining sugar, softened butter, optional egg, and proofed yeast mixture until dough forms. Knead 5-8 minutes until smooth and elastic. Place dough in greased bowl, cover, and let rise in warm spot 1 hour until doubled.
2.5 cups all-purpose flour, 0.25 cup granulated sugar, 0.25 cup butter, 1 large egg, 2.25 tsp active dry yeast, 0.75 cup milk
Punch down dough. Roll dough on floured surface into 12x8 inch rectangle. Spread 2 tablespoon softened butter evenly over dough. Sprinkle brown sugar and cinnamon evenly on top. Roll tightly from long side and cut into 6-8 equal slices.
2 tbsp butter, 0.33 cup brown sugar, 2 tsp ground cinnamon
Preheat air fryer to 350°F for 3 minutes. Cut parchment paper to fit basket. Place rolls cut-side up in basket spaced 1 inch apart. Cook rolls 12-15 minutes until golden brown and cooked through. Test with toothpick; it should come out clean.
While rolls cook, whisk sifted powdered sugar, milk, and vanilla extract until smooth. Pour glaze over warm rolls immediately after removing from air fryer so it soaks in and sets with a shiny finish.
1 cup powdered sugar, 2 tbsp milk, 0.5 tsp vanilla extract