- Mix the yeast, water, sugar, and flour in a medium bowl until combined. Cover with plastic wrap and let rise until foaming (should double in size).
- Combine 3 cups flour, salt, and sugar in a food processor and mix until combined. Add melted butter and sponge mixture.
- Combine lightly beaten egg with cooled milk. With the processor running, pour in egg-milk mixture until dough is sticky. Add additional flour until dough forms a ball.
- Place the dough into a large bowl, cover with a kitchen linen, and set aside until dough triples in volume. Remove dough from the bowl and transfer to a lightly floured board.
- Shape into butterfly rolls: divide the dough in half, roll each half into a 15×8-inch rectangle. Brush with melted butter and sprinkle with chopped fresh rosemary. Roll up the longest side tightly. Cut crosswise into 1½-inch pieces.
- Put rolls on a buttered baking sheet, tucking the end pieces, and place 1 inch apart. Cover rolls and let rise until doubled in size.
- Preheat oven to 400 degrees. Mix 1 egg yolk and 2 tablespoons heavy cream until combined. Brush egg-cream mixture over tops of rolls. Bake 15 minutes or until golden brown. Cool on a rack or serve hot from the oven!