Start the Preferment: In a mixing bowl, stir together the flour, yeast, and warm water until blended with no dry spots. Cover and let rest for an hour until bubbly.
Mix the Dough: Add the rest of the dough ingredients to the preferment. Mix on low until combined and shaggy, about 2 minutes. Scrape down the sides, then knead on medium-high until the dough is elastic and smooth, roughly 8–10 minutes. Dough will be sticky, so scrape as needed. Cover and let rise in a warm area until doubled in size, about 1 to 1½ hours.
Make the Cookie Topping: Cream together the sugar, butter, vanilla, and salt until smooth. Add the flour to form a soft dough. Divide into 10 pieces (about 1 ounce each) and flatten each into a 3–4 inch disk between wax paper or with a rolling pin. Set aside.
Shape the Dough: Lightly flour your work surface and turn out the dough. Divide into 10 pieces (around 3 ounces each), deflate gently, then shape into balls. Place seam side down on a floured surface.
Second Rise: Use your hands to tighten each ball into a smooth round. Arrange 5 per baking sheet lined with parchment. Cover and rest until puffy, about 30–45 minutes. A floured finger should leave an impression.
Preheat the Oven: Set your oven to 350°F and position racks in upper and lower thirds.
Top the Rolls: Lightly brush each dough ball with egg white, place a cookie disk on top, and score the topping using a knife or baker’s lame in a spiral or crosshatch pattern.
Bake: Place in the oven and bake until golden brown, rotating pans halfway through, about 18 to 24 minutes.
Cool and Serve: Let the conchas cool on the tray until they're safe to handle. Enjoy warm or at room temperature. Store leftovers in an airtight wrap for up to 3 days, or freeze for a month.