Mix gluten-free flour, instant yeast, salt, garlic powder, and warm water in a stand mixer with the flat beater attachment on speed #2 for five minutes.
Add olive oil to the dough and mix on the lowest speed for two minutes. Let dough rest in the refrigerator for 10 minutes.
Lightly dust your counter and dough with gluten-free flour or cornstarch as needed. Press or roll the dough to form it into a log approximately 12" long. Cut the log into 8 even pieces.
Roll and pull each piece of dough with your hands until it forms a rope about 8" long.
Gently tie each rope into a knot and tuck the two ends of the rope under the knot. Place tied knots onto a baking pan lined with a silicone mat or parchment paper for easy cleanup.
Lightly spray the underside of a sheet of plastic wrap with cooking spray to prevent sticking, and cover the baking sheet. Let the dough rise for two hours in a warm place until the knots have doubled in size. (See notes for 1-hour quick-rise or 8-24 hour slow-rise options)
Towards the end of the rising time, combine butter, garlic, and parsley (and optional parmesan) in a small frying pan or saucepan over medium/low heat for approximately five minutes until butter is melted and flavors combine.
When garlic knots are done rising, preheat oven to 400℉ and remove plastic wrap or towel. Brush half of the garlic-butter mixture onto the knots and reserve the other half for after baking.
Bake garlic knots for approximately 25 minutes until light golden brown.
Remove from the oven when knots are golden brown and brush generously with the remaining garlic-butter topping. Serve.