In the bowl of an electric stand mixer, combine flour, salt, and 3 tablespoons of sugar. Mix these dry ingredients well with a whisk. This ensures that the yeast will work properly and that the flavors are evenly distributed.
In a small bowl, place warm water and sprinkle the yeast and the remaining 1 teaspoon of sugar on top. Stir gently and allow the mixture to sit for about five minutes until it becomes frothy. This is your activation step, ensuring the yeast is alive and well!
Once frothy, add the yeast mixture along with buttermilk, 1 egg, and softened butter into the mixing bowl. Using the paddle attachment, beat until everything comes together into a sticky dough.
Switch to the dough hook and knead at medium speed for about seven minutes. You want the dough to be smooth and elastic. It should pull away from the sides of the bowl but still be slightly tacky to the touch.
Transfer the dough to a bowl greased with vegetable oil, turning it to coat. Cover it with plastic wrap or a clean kitchen towel and let it rise until doubled in size, which usually takes about one and a half hours. Ideal room temperature for rising is around seventy-five degrees Fahrenheit.
Once risen, lightly flour your work surface and divide the dough into sixteen even pieces. Shape each piece into a rope approximately seven to eight inches long. At this stage, you can choose to make knots or spirals. For knots, shape the dough like a pretzel and tuck the ends underneath.
Arrange the shaped rolls on a large baking sheet lined with parchment paper. Cover them again with plastic wrap or a towel and let rise for another forty-five to sixty minutes, allowing them to puff up beautifully.
Preheat your oven to 350 degrees Fahrenheit while waiting for the rolls to rise. This ensures they bake evenly and thoroughly.
In a small bowl, lightly beat the remaining egg. Brush this egg wash over the tops of the rolls for that beautiful golden color.
Bake the rolls in the preheated oven for about fifteen minutes, or until they are lightly browned and sound hollow when tapped. Keep an eye on them towards the end to ensure they don’t over-bake.
For the finishing touch, place all topping ingredients in a small bowl and microwave until the butter is melted. Once the rolls come out of the oven, brush them generously with this melted butter mixture to enhance the flavor and create a lovely sheen.