Melt the butter in a small skillet over medium heat. Add the green garlic and salt and sauté until the garlic begins to soften, about 2-3 minutes. Add the hot pepper flakes and continue to cook for another 30 seconds. Remove from the heat, stir in the chopped parsley and set aside.
To make the dough knots, divide the pizza dough into about 18-24 pieces, depending on how big you want your garlic knots. To make a knot, take one piece and stretch it into or roll it into a 4-inch rope, twist around your fingers and tie into a knot. Repeat with remaining dough.
Drizzle the olive oil in a large cast iron skillet or oven-proof pan, spreading it in an even layer on the bottom of the pan. Transfer the knots to the skillet, arranging them in concentric circles, about a 1/2 inch apart. Cover with a clean kitchen towel and let proof until they are about 1 1/2-2 times their original size, about 30-45 minutes.
While the dough knots are proofing, preheat the oven to 425°F.
Spoon the reserved green garlic and butter mixture over the dough knots. Sprinkle the grated mozzarella and Parmigiano-Reggiano cheese in an even blanket over the garlic dough knots. Don’t worry if some gets in between the knots, that cheese will melt and crisp into delicious cheese skirty bits. Bake until cooked through and the cheese is melted and golden brown on top, about 15-20 minutes, depending on the size of your garlic knots.
Allow to cool for 5 minutes. Garnish with extra hot pepper flakes and chopped parsley, if desired, and serve hot or warm.
