In the bowl of a stand mixer, combine 4 cups all-purpose flour, 1 1/2 teaspoons kosher salt, and 3 tablespoons sugar.
In a small bowl, stir together 1/4 cup warm water (105–110°F), 1 (1/4-ounce) packet active dry yeast, and 1 teaspoon sugar. Let sit about 5 minutes, until foamy.
Add the yeast mixture, 1 cup room-temperature buttermilk, 1 large egg (reserve the other egg), and 1/4 cup softened unsalted butter to the flour mixture. Using the paddle attachment, mix on low/medium until the dough comes together and pulls away from the sides of the bowl.
Switch to the dough hook and knead on medium speed for 7 minutes, until the dough is smooth and elastic. (If you do not have a stand mixer, turn the dough onto a lightly floured surface and knead by hand for 8–10 minutes.)
Lightly grease a clean bowl. Transfer the dough to the bowl and turn to coat. Cover with plastic wrap or a clean kitchen towel and let rise in a warm place until doubled in size, about 1 1/2 hours.
Lightly flour a work surface. Gently deflate the dough and divide it into 16 equal pieces.
Roll each piece into a rope about 7–8 inches long. Shape each rope into either a knot (form a pretzel shape and tuck the ends under) or a spiral (coil the rope around itself).
Place the shaped rolls on a large baking sheet lined with parchment paper, leaving space between them for expansion. Cover loosely with plastic wrap or a kitchen towel and let rise until puffy, about 45–60 minutes. Begin preheating the oven to 350°F during the last 15 minutes of this rise.
Lightly beat the reserved egg in a small bowl. Brush the tops of the risen rolls with the beaten egg.
Bake the rolls in the preheated 350°F oven for about 15 minutes, or until the rolls are light golden brown.
While the rolls bake, combine the topping ingredients in a small microwave-safe bowl: 1/4 cup unsalted butter, 2 tablespoons chopped fresh parsley, 2 teaspoons chopped fresh rosemary, 1/4 teaspoon garlic powder, and 1/4 teaspoon kosher salt. Microwave until the butter is melted, then stir to combine.
Remove the rolls from the oven and immediately brush them with the butter-herb mixture. Let the rolls cool slightly before serving.