Bring the sugar and water to a boil in a saucepan over medium heat. Once the caramelized sugar has browned, remove the pan from the heat and let the mixture cool until the bubbles have disappeared. Place 4 ramekins in a casserole dish and divide the caramelized sugar between the ramekins, making sure to save some back for the spun sugar cages.
Whisk the milk and vanilla in a saucepan over medium heat and bring to a boil. Pour the vanilla milk into a large bowl and whisk in the sugar and eggs. Divide the mixture between the 4 ramekins and pour over the cooled caramel bases.
Fill the casserole dish halfway with hot water, transfer the dish to a preheated oven, and cook at 350°F for 25 minutes.
Once the flan has cooled a bit, carefully transfer the ramekins to the refrigerator and chill for 1½ hours.
Grease the outsides of 4 ramekins and place them upside-down on parchment paper. Use a wooden spoon to drizzle the remaining caramelized sugar back and forth in a zigzag pattern over each ramekin. Let the spun sugar cages harden and carefully cut away the excess threads around each ramekin.
Carefully flip the creme caramel flans over onto small plates and place the spun sugar cages on top.
