In bowl of a stand mixer, whisk flour paste and milk until smooth. Add egg and whisk until incorporated. Add flour and yeast. Fit stand mixer with dough hook and mix on low speed until all flour is moistened, 1 to 2 minutes. Let stand for 15 minutes.
Add sugar and salt and mix on medium-low speed for 5 minutes. With mixer running, add softened butter, 1 piece at a time. Continue to mix on medium-low speed 5 minutes longer, scraping down dough hook and sides of bowl occasionally (dough will stick to bottom of bowl).
Transfer dough to very lightly floured counter. Knead briefly to form ball and transfer, seam side down, to lightly greased bowl; lightly coat surface of dough with oil spray and cover witl1 plastic wrap. Let rise until doubled in volume, about 1 hour.
Grease 9-inch round cake pan and set aside. Transfer dough to counter. Press dough gently but firmly to expel all air. Pat and stretch dough to form 8 by 9-inch rectangle with short side facing you. Cut dough lengthwise into 4 equal strips and cut each strip crosswise into 3 equal pieces. Working with 1 piece at a time, stretch and press dough gently to form 8 by 2-inch trip. Starting on short side, roll dough to form snug cylinder. Arrange shaped rolls seam side down in prepared pan, placing 10 rolls around edge of pan, pointing inward, and remaining 2 rolls in center. Cover with plastic and let rise w1til doubled, 45 minutes to 1 hour.
When rolls are nearly doubled, adjust oven rack to lowest position and heat oven to 375 degrees. Bake rolls until deep golden brown, 25 to 30 minutes. Let rolls cool in pan on wire rack for 3 minutes; invert rolls onto rack, tl1en reinvert. Brush tops and sides of rolls with melted butter. Let rolls cool for at least 20 minutes before serving.
