Position a rack in the center of the oven and preheat it to 400°F (205°C). Generously grease all 24 cups of a metal mini muffin pan with the softened butter, covering the bottoms and sides.

Place the cold mashed potatoes in a large bowl. They should be thick enough to hold a mound on a spoon. If they are runny or spread quickly, stir in 1 additional tablespoon of flour before adding the remaining ingredients.

Add the lightly beaten eggs to the mashed potatoes. Stir until the mixture is smooth and evenly combined, with no visible streaks of egg.

Reserve 1/4 cup (30 g) cheddar and 2 tablespoons (10 g) Parmesan for topping. Add the remaining cheddar and Parmesan to the potato mixture along with the flour, chives, baking powder, salt, black pepper, and garlic powder.

Fold the ingredients together until evenly distributed. The mixture should be thick, scoopable, and slightly sticky. If it looks loose enough to pour, add another tablespoon of flour.

Divide the potato mixture evenly among the 24 prepared mini muffin cups, using about 1 heaping tablespoon per cup. The mixture can rise just above the rim. Smooth the tops lightly without compressing them.

Sprinkle the reserved cheddar and Parmesan evenly over the puffs. Keep most of the cheese on the potato mixture rather than on the exposed pan, where it may burn.

Bake for 22 to 26 minutes, rotating the pan after 15 minutes. The puffs are ready when the tops are golden, the edges are deeply browned, and the centers feel set rather than wet. An instant-read thermometer inserted into the center should register at least 160°F (71°C).

Let the puffs cool in the pan for 10 minutes. They will firm as they rest and release more cleanly than they would straight from the oven.

Run a thin butter knife or small offset spatula around the edge of each puff. Lift them carefully from the pan and serve warm with sour cream and additional chives, if using.