Heat a 10-inch nonstick skillet over moderately high heat. Add 1 teaspoon of oil to the center of the pan and immediately pour 1/4 cup of the batter directly onto the oil; the batter will spatter and spread on its own, forming a lacy crepe. (If the batter doesn't spread, thin it with club soda, adding 2 tablespoons at a time.) Cook the dosa until browned at the edge and dry on the surface, about 2 minutes. Gently flip the dosa with a spatula and cook until the browned on the second side, about 1 minute longer. Transfer the dosa to a baking sheet. Repeat with the remaining batter and oil, placing the finished dosas on the baking sheet but not stacking them as they will stick together. You should have about 12 dosas.