Simmer potatoes and garlic in salted water until tender, about 10 minutes. Drain, and pass hot potatoes and garlic through a ricer or a food mill. Stir in cheese and 4 tablespoons butter, then the cream. Season with salt and pepper.
Place 1 heaping tablespoon potato mixture onto center of bottom half of each round. Brush edges with water. Fold top half over filling, and press to force out air and seal. Repeat.
Bring remaining tablespoon butter and the water to a simmer in a large nonstick skillet over medium heat. Add pierogi, cover, and steam for 4 minutes. Uncover, and brown until golden, about 3 minutes per side. Top with chives.