To Make the Dough: Warm a small bowl in hot water. Add 1 tablespoon of sugar and the warm water to the bowl. Sprinkle yeast over the water, but do not stir. Cover the bowl with a saucer, and let stand for 3 to 5 minutes. This is called “proofing the yeast”. It should start to develop some bubbles and foam. After the few minutes have passed, stir and cover again for another 2 to 3 minutes. Mixture should be more foamy.
Using a stand mixer with the paddle attachment, mix the flour, remaining 3 tablespoons of sugar and the salt. Add the cubed vegan butter and mix until blended and sandy crumbs have formed. Takes about 2 to 4 minutes, depending on the temperature of the vegan butter.
In a separate bowl, whisk together with a fork the milk and vanilla. With the mixer turned on, slowly add the milk and the dissolved yeast and water to the flour. Mix on low speed for about 15 seconds, then scrape down the sides. Mix for another 30 seconds until a soft dough is formed. Transfer dough to a lightly oiled, medium bowl. Using your hands, spread a thin layer of oil over the top of the dough, then cover tightly with plastic wrap. Refrigerate overnight.
To Make the Topping: First, remove the dough from the refrigerator so it warms up just a bit. Have muffin pans nearby: you'll need enough for 15 buns. If you don’t have enough pans to bake all the buns at once, rinse your tins after the first batch and repeat the process. In a small bowl, mix together the vegan butter, brown sugar, maple syrup, and corn syrup to make a paste. Using the back of a spoon, spread about 2 teaspoons into each cavity of the muffin pan. Coat the bottom and about three-fourths of the way up the sides of each cavity. Finish by sprinkling the chopped pecans into each coated cavity.
To Fill the Buns: Mix together in a small bowl the sugar, brown sugar, and cinnamon. Set aside. Lightly flour a clean workspace large enough to roll out the dough. Remove the dough from the bowl and flatten gently with floured hands until you have a rectangle about 4 inches by 6 inches. With a rolling pin, roll out the dough till it’s 10 inches by 15 inches, making the longest side parallel to the edge of the counter.
Using a small offset spatula, or butter knife, spread the softened butter to cover the dough, leaving an inch border along the top border, opposite the side closest to you. Sprinkle the sugar-cinnamon mixture over the dough, leaving a one-inch border at the top. Moisten a finger with water and go over the top border so that it will seal when rolled.
To Roll and Shape the Buns: Preheat oven to 350°F. Starting with the side closest to you, roll the dough in a log away from you. Try to keep it tight. Gently press and roll till you reach the border at the top. Press/pinch the moistened border so that a seal is formed along the length of the log. Gently pinch the ends shut. With a sharp knife, mark/score the dough with 14 lines, which will yield 15 buns when cut. Cut through the dough on the score lines and carefully place each slice into the prepared muffin tin. Press down gently. Cover with a clean dish towel and set the muffin tins on top of the warm stove to rest for 45 minutes. The dough should be nearly doubled in size when ready.
Bake the buns, rotating the pans halfway through, for 18 to 20 minutes, or until they begin to turn a golden brown. While the buns are baking, place the parchment paper underneath two cooling racks. Remove the buns from the oven, and carefully flip the pans upside down onto the racks. The topping will coat the buns while pans are in the inverted position. Let sit upside down for a minute or two, then carefully lift the pans off. Don’t leave it too long or you’ll end up with more topping in the pan than on the muffin. Scoop out any remaining topping and spread on the appropriate bun.
