In the bowl of a stand mixer fitted with the paddle attachment, beat 1 cup (125g) flour, sugar, 1 tablespoon (9g) salt, yeast, 1/2 teaspoon (1.5g) garlic powder, and baking soda at low speed until combined.
In a medium saucepan, heat 3/4 cup (180g) water, sour cream, and 3 tablespoons (42g) butter over medium-low heat, stirring frequently, until butter is melted and an instant-read thermometer registers 120°F (49°C) to 130°F (54°C). Add warm sour cream mixture to flour mixture; beat at medium-low speed until combined, about 1 minute, stopping to scrape sides of bowl. With mixer on low speed, gradually add 2 1/4 cups (281g) flour and 1/2 cup (55g) green onion, beating just until combined and stopping to scrape sides of bowl.
Switch to the dough hook attachment. Beat at low speed until a soft, somewhat sticky dough forms, 10 to 12 minutes, stopping to scrape sides of bowl and dough hook; add up to remaining 1/4 cup (31g) flour, 1 tablespoon (8g) at a time, if dough is too sticky. (Dough will mostly pull away from sides of bowl and should pass the windowpane test; see Note.) Turn out dough onto a lightly floured surface, and shape into a smooth round.
Lightly oil a large bowl. Place dough in bowl, turning to grease top. Cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, 30 to 45 minutes.
Preheat oven to 375°F (190°C). Spray a 12-cup muffin pan with cooking spray.
In a small microwave-safe bowl, heat remaining 5 tablespoons (70g) butter on high in 10-second intervals until melted.
Punch down dough; cover and let stand for 10 minutes. Divide dough in half, covering one portion with plastic wrap. On a lightly floured surface, roll uncovered half into a 12-inch square. Brush with 1 tablespoon (14g) melted butter. Using a pizza cutter, cut dough into 12 (6x2-inch) strips. Stack 6 strips, butter side up; repeat with remaining 6 strips to create a separate stack. Using a floured serrated knife, cut each stack crosswise into 3 (2-inch) squares. Place each square stack, layered side up, in prepared muffin cups. Repeat procedure with remaining dough and 1 tablespoon (14g) melted butter. Slightly separate layers of each fantail. Cover loosely with plastic wrap, and let rise in a warm, draft-free place (75°F/24°C) until dough fills cups, 15 to 25 minutes.
In a small bowl, whisk together egg and remaining 1 tablespoon (15g) water. Brush tops of dough with egg wash.
Bake until lightly golden, 12 to 15 minutes.
Add remaining 1 tablespoon (7g) green onion, remaining 1/2 teaspoon (1.5g) garlic powder, and remaining 1/4 teaspoon salt to remaining melted butter, stirring until combined. Carefully remove fantails from pan; brush with butter mixture. Let cool for 10 minutes before serving.