Mix the sugars and cinnamon together in a bowl. If necessary, in another bowl, work the butter with a spatula until it is soft, smooth and spreadable
To Shape the Buns: On a flour-dusted work surface, roll the chilled dough into a 16-inch square. Using your fingers or a pastry brush, spread the softened butter over the dough. Sprinkle the dough with cinnamon sugar, leaving a 1-inch strip bare on the side farthest from you. Starting with the side nearest you, roll the dough into a cylinder, keeping the roll as tight as you can. (At this point, you can wrap the dough airtight and freeze it for up to 2 months. Or, if you want to make just part of the recipe now, you can use as much of the dough as you’d like and freeze the remainder. Reduce the glaze recipe accordingly.)
With a chef’s knife, using a gentle, sawing motion, trim just a tiny bit from the ends of the roll if they’re very ragged or not well filled, then cut the log into 1-inch-thick buns. (Because you trim the ragged ends of the dough, and you may have lost a little length in the rolling, you will get 15 buns, not 16.) Fit the buns into the pan cut side down, leaving some space between them.
Lightly cover the pan with a piece of wax paper and set the pan in a warm place until the buns have doubled in volume, about 1 hour and 45 minutes. The buns are properly risen when they are puffy, soft, doubled and in all likelihood touching one another.
Getting Ready to Bake: When the buns have almost fully risen, center a rack in the oven and preheat the oven to 375 degrees F.
Remove the sheet of wax paper and put the pan on a baking sheet lined with parchment or a silicone mat. Bake the sticky buns for about 30 minutes, or until they are puffed and gorgeously golden; the glaze will be bubbling away merrily. Pull the pan from the oven.
The sticky buns must be unmolded minutes after they come out of the oven. If you do not have a rimmed platter large enough to hold them, use a baking sheet lined with a silicone mat or buttered foil. Be careful – the glaze is super-hot and super-sticky.
Golden Brioche Loves
Put the yeast, water and milk in the bowl of a stand mixer and using a wooden spoon, stir until the yeast is dissolved. Add the flour and salt, and fit the mixer with the dough hook, if you have one. Toss a kitchen towel over the mixer, covering the bowl as completely as you can – this will help keep you, the counter and your kitchen floor from being showered in flour (yes, you can peek to see how you’re doing), then remove the towel, increase the mixer speed to medium-low and mix for a minute or two, just until the flour is moistened. At this point you’ll have a fairly dry, shaggy mass.
Scrape the side and bottom of the bowl with a rubber spatula, set the mixer to low and add the eggs, followed by the sugar. Increase the mixer speed to medium and beat for about 3 minutes, until the dough forms a ball. Reduce the speed to low and add the butter in 2-tablespoon-size chunk, beating until each piece is almost incorporated before adding the next. You’ll have a dough that is very soft, almost like a batter. Increase the speed to medium-high and continue to beat until the dough pulls away from the sides of the bowl, about 10 minutes.
Transfer the dough to a clean bowl (or wash out the mixer bowl and use it), cover with plastic wrap and leave at room temperature until nearly doubled in size, 40 – 60 minutes, depending upon the warmth of your room.
Deflate the dough by lifting it up around the edges and letting it fall with a slap into the bowl. Cover the bowl with plastic wrap and put it in the refrigerator. Slap the dough down in the bowl every 30 minutes until it stops rising, about 2 hours, then leave the covered dough in the refrigerator to chill overnight.