Loaves and buns can be baked up to two weeks ahead and frozen until ready to use.
In small bowl, sprinkle yeast and 1/2 teaspoon sugar over 1/2 cup warm water; stir. Let stand until foamy, about 5 minutes.
In bowl of electric mixer fitted with paddle, beat remaining 1 1/4 cups warm water, egg, powdered milk, 2 tablespoons sugar, salt, and 1 cup flour. Beat until smooth and creamy, about 7 minutes.
Add yeast mixture; beat on medium. On medium-low, beat in 3 1/2 cups flour, 1/2 cup at a time, until dough comes together (it will be sticky), about 2 minutes. Switch to dough hook. Gradually add butter; beat until dough is soft and sticks to fingers slightly, about 7 minutes. If dough is too wet, add 1/4 cup flour.
On lightly floured surface, knead dough several turns into a ball. Coat bowl with spray; add dough smooth side up. Cover dough with sprayed plastic wrap. Let stand in warm place until doubled, about 1 hour. Shape and bake per recipes above.