Set a 10-inch nonstick skillet over moderate heat and brush with butter. Pour in a scant 1/3 cup of the batter and swirl to coat the pan. Cook the blini until tiny bubbles form on the surface and the bottom is browned, 2 minutes. Carefully flip the blini and cook until the bottom is lightly browned in spots, 30 seconds. Transfer to a baking sheet. Repeat with the remaining batter, buttering the pan and whisking in 1 or 2 tablespoons of milk to thin the batter as needed. You should have about 13 blini. Let cool slightly.