Whisk water and flour together in a small bowl until no lumps remain. Microwave, whisking every 25 seconds until mixture thickens to stiff, smooth, pudding-like consistency that forms mound when dropped from the end of whisk into a bowl, 50 to 75 seconds.

For the Dough

In the bowl of a stand mixer, whisk flour paste and milk together until smooth. Add egg and yolk and whisk until incorporated. Add flour and yeast. Fit stand mixer with a 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 fro 5 minutes. Stop the mixer and add butter. Continue to mix on medium-low speed for 5 minutes longer, scraping down dough hook and sides of the bowl halfway through (dough will stick to the bottom of the bowl).

Transfer dough to a lightly floured counter. Knead briefly to form a ball and transfer seam side down to lightly greased bowl; lightly coat the surface of dough with vegetable oil spray and cover bowl with plastic wrap. Let dough rise until just doubled in volume, 40 minutes to 1 hour.

While dough rises, grease 13 by the 9-inch metal baking pan. Whisk melted butter, brown sugar, granulated sugar, corn syrup, and salt together in a medium bowl until smooth. Add water and whisk until incorporated. Pour mixture into prepared pan and tilt pan to cover the bottom. Sprinkle evenly with pecans, if using.

Turn out dough onto a lightly floured counter. Press dough gently but firmly to expel air. Working from the center toward edge, pat and stretch dough to form 18 by 15-inch rectangle with the long edge nearest you. Sprinkle filling over the dough, leaving a 1-inch border along top edge; smooth filling into even layer with your hand, then gently press mixture into the dough to adhere.

Bake buns on upper rack until golden brown, about 20 minutes. Tent with aluminum foil and bake until the center of dough registers at least 200 degrees, 10 to 15 minutes longer. Let buns cool in pan on a wire rack for 5 minutes. Place a rimmed baking sheet over buns and carefully invert. Remove pan and let buns cool for 5 minutes. Using a spoon, scoop any glaze on the baking sheet onto buns. Let cool for at least 10 minutes longer before serving