Divide the dough into 8 even pieces. Use your hands to roll each piece into a 6-inch-long tube, then tie each into a knot. Arrange the knots on a parchment-lined baking sheet. Bake until golden brown all over, 7 to 8 minutes.
Meanwhile, melt the butter over medium-low heat in a small saucepan. Add the garlic, red pepper flakes and a rounded 1/4 teaspoon salt and cook, stirring often, until the garlic is pale golden, about 3 minutes. Take off the heat and stir in the parsley.
Brush the garlic knots generously with the garlic butter and sprinkle with a little grated Parmesan. Transfer the remaining butter to a small bowl.