In a medium bowl, whisk together the eggs, milk, butter, and vanilla. Set aside.

In a large bowl, mix together the flour, sugar, baking powder, and salt. Make a well in the center of the dry ingredients, then pour in the egg mixture. Whisk until mostly smooth, with just a few lumps. (Note: The batter will be quite thin)

Preheat a waffle maker.

Ladle the batter into the waffle maker, using 1/2 to 3/4 cup batter and spreading it so that it almost reaches the edges of the waffle maker. Cook until the waffles are crisp and browned, 3 to 4 minutes.

Using a spatula, remove the waffles from the waffle maker and serve right away or place on a baking sheet in a single layer in a 95°C oven to keep warm for up to 20 minutes.

In a small saucepan over medium-low heat, warm the cream until bubbles form around the sides of the pan. Do not allow the cream to boil. Remove from the heat and cover to keep warm.

Place the sugar and cold water in a high-sided saucepan. Cook over medium heat, stirring until the sugar dissolves. Stop stirring and let the syrup slowly boil, brushing any sugar down from the sides of the pan with a wet pastry brush. Cook until the syrup turns light brown, 10 to 15 minutes.

Whisking the caramel constantly, add the warm cream. Return the pan of caramel to low heat and cook, whisking, until completely smooth, 2 to 3 minutes.

Remove the pan from the heat and add the vanilla and salt to taste.