How to Make It
Stir together 3 tablespoons warm water, yeast, and 1 teaspoon granulated sugar in a small bowl; let stand until foamy, about 5 minutes.
Beat salt, 1/3 cup granulated sugar, and 6 tablespoons butter with a stand mixer fitted with paddle attachment on medium speed until light and fluffy, 3 to 4 minutes. Add milk, egg, and yeast mixture; beat on low speed until incorporated, about 20 seconds, stopping to scrape sides of bowl as needed. (Mixture will look broken at this point.) With mixer running on low speed, gradually add flour, beating until all flour is incorporated, about 3 minutes. Remove paddle attachment, and replace with dough hook. Continue beating on medium speed until dough is smooth, elastic, and tacky, about 5 minutes. Spray a medium bowl lightly with cooking spray; add dough, and cover tightly with plastic wrap. Chill at least 8 hours or up to overnight.
Turn dough out on a lightly floured surface. Gently roll into an 18- x 12-inch rectangle (about 1/4 inch thick). Spread remaining 6 tablespoons very soft butter onto dough. Stir together brown sugar, cinnamon, and remaining 1/3 cup granulated sugar; sprinkle mixture evenly over butter, pressing lightly to adhere. Starting with 1 long side, tightly roll dough, jelly-roll fashion. Using a serrated knife or unflavored floss, cut roll crosswise into 14 (1 1/2-inch-wide) slices.
Line 2 (8-inch) round pans with parchment paper; spray lightly with cooking spray. Place slices, cut sides up, into prepared pans. Cover loosely with plastic wrap, and let stand at room temperature until almost doubled in size, 45 minutes to 1 hour and 15 minutes.
Preheat oven to 350°F. Bake roses in preheated oven until light golden brown, 22 to 26 minutes. Carefully transfer roses from pan to a wire rack. Serve warm.
To prepare these in a 9- x 13-inch baking pan or in a 12-cup muffin pan, cut roll into 12 slices, and place slices in a greased parchment-lined pan or muffin cups. Bake as directed.