In the bowl of a stand mixer fitted with the paddle attachment, combine 1½ cups (188 grams) flour, sugar, yeast, and kosher salt.
In a medium saucepan, heat 1 cup (240 grams) water, sour cream, and 1⁄4 cup (57 grams) melted butter over medium heat until an instant-read thermometer registers 120°F (49°C) to 130°F (54°C). Add warm sour cream mixture to flour mixture, and beat at medium speed until combined. Beat in 1 egg (50 grams) until combined. With mixer on low speed, gradually add 3¼ cups (406 grams) flour, chives, and dill, beating just until a shaggy dough forms.
Switch to the dough hook attachment. Beat at low speed until a soft, somewhat sticky dough forms, 7 to 8 minutes, stopping to scrape sides of bowl and dough hook. Add up to remaining 1⁄4 cup (31 grams) flour, 1 tablespoon (8 grams) at a time, if dough is too sticky. Cover and let stand in a warm, draft-free place (75°F/24°C) for 10 minutes. (Dough will puff slightly.)
Line a 13×9-inch baking sheet with parchment paper.
Divide dough into 12 portions (about 93 grams each). With lightly floured hands, roll 1 portion into a 12-inch-long rope. (Keep remaining dough covered to prevent it from drying out.) Tie a loose knot toward one end of rope, leaving about 1 inch on one end. Pinch together both ends of dough under knot, forming a knotted ball. Place, seam side down, on prepared pan. Cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, 20 to 30 minutes.
Preheat oven to 375°F (190°C).
In a small bowl, whisk together remaining 1 egg (50 grams) and remaining 1 tablespoon (15 grams) water. Brush tops of dough with egg wash.
Bake until golden brown and an instant-read thermometer inserted in center registers 190°F (88°C), 20 to 25 minutes, covering with foil to prevent excess browning, if necessary.
In a small bowl, stir together garlic salt and remaining 2 tablespoons (28 grams) melted butter; brush onto rolls. Serve warm.