In a medium microwave-safe bowl, microwave ¼ cup beer until it reaches 105°F to 110°F, about 10 seconds. Stir together warm beer, yeast, and sugar; let stand until mixture is foamy, about 5 minutes. Stir in 6 tablespoons (84 grams) melted butter and remaining ¾ cup beer.
In the bowl of a stand mixer fitted with the paddle attachment, beat 2 cups (250 grams) flour, half of garlic, 3 tablespoons parsley, Parmesan, and salt at medium speed until combined. Add yeast mixture, beating to combine, about 1 minute. Gradually add remaining 1 cup (125 grams) flour, beating until dough begins to pull away from sides of bowl, about 3 minutes. Cover with plastic wrap, and let rise in a warm, draft-free place (75°F) for 45 minutes.
Spray a 12-cup muffin pan with cooking spray.
Punch down dough, and divide in half. Pat one half into a square. On a lightly floured surface, using a floured rolling pin, roll dough into a 12-inch square. Sprinkle with half of Gouda, and press into dough. Using a sharp knife, cut dough into 6 equal strips. Stack strips, cheese side up; cut crosswise into 6 equal pieces. Place each piece on its side in prepared muffin cups. Repeat with remaining dough and Gouda.
Slightly separate layers of each roll. Cover loosely with plastic wrap, and let rise in a warm, draft-free place (75°F) until dough fills cups, 30 to 45 minutes.
Preheat oven to 375°F. Bake until golden brown, 20 to 24 minutes.
In a small saucepan, melt remaining 2 tablespoons (28 grams) butter over medium heat. Add remaining garlic and remaining 1 tablespoon parsley. Cook until fragrant. Brush warm fantails with butter mixture. Let cool for at least 10 minutes before serving.
Recipe by Bake from Scratch at https://staging.bakefromscratch.com/parmesan-gouda-fantails/