In a medium saucepan, heat the sugar over medium heat, stirring constantly with a silicone spatula until a golden caramel forms.
Turn off the heat and carefully pour ¼ cup of boiling water over the caramel. Be careful, as the syrup will bubble vigorously. Return the saucepan to medium heat and stir the caramel with the spatula until smooth again.
Turn off the heat and transfer the caramel syrup to a 1.5-qt flan mold with a lid. Using a dish towel, hold the mold and swirl to coat the sides evenly with the caramel. Repeat, and set the mold aside.
In a large bowl or blender, combine the condensed milk, water, and plain yogurt. Whisk or blend the mixture for 2 minutes until smooth and well combined.
Pour the blended mixture into the caramel-coated mold.
Cover the mold with its lid or aluminum foil. Place the covered mold inside a pot. Add three cups of water to the pot. Optionally, add a little vinegar or lemon juice to the water to prevent the pot from darkening. Cover the pot and turn on the stove. Bring the water to a boil. Once boiling, reduce the heat to low and cook for 30 minutes. After 30 minutes, turn off the heat and carefully remove the mold from the pot.
Place the mold on a cloth and refrigerate for at least 6 hours or until well chilled.
After chilling, run a knife around the edges of the flan to loosen it. Tilt the mold slightly to let air in. Place a plate on top of the mold and flip it over to release the flan.
Heat the remaining caramel on the stove. Add three tablespoons of water to the caramel and stir until it melts again. Boil the caramel for two minutes, then pour it over the flan. Let the bubbles settle before serving.