To make the dulce de leche, gently heat ¼ cup granulated sugar in a saucepan over medium heat until it has melted. Don't stir the sugar while it is melting — just tip the pan to move it around.
Once the sugar has melted, add ¼ cup of cold butter, and stir quickly. The mixture will bubble up as the butter is incorporated. Then, slowly pour in ⅓ cup of milk, stirring as you pour.
Finally, add the condensed milk, and simmer for 10 minutes, stirring frequently. Once the dulce de leche is a deep golden color and has thickened, remove it from the heat, cool, and pour into an airtight container.
Preheat the oven to 425 F, and line a baking tray with foil. While the oven preheats, make the crepe batter. Whisk the flour, remaining 1 tablespoon of sugar, and a pinch of salt in a medium bowl.
Make a well in the flour mixture, and add the eggs to the bowl. Whisk everything together until a smooth, thick paste forms. Slowly incorporate the remaining 1 cup of milk and cold water a little at a time, whisking in between each addition. Set the finished crepe batter in the fridge until you are ready to use it.
Add the pineapple slices to a bowl, and toss with the brown sugar and the cinnamon. Transfer it to the prepared baking tray, and dot 3 tablespoons of cubed butter around the pineapple. Bake for 20 minutes, turning once halfway through.
While the pineapple cooks, heat up a large, shallow frying pan or crepe pan to a medium-high. When the pan is heated, grease the pan with a little of the remaining butter. Then, add roughly ¼ cup of crepe batter to the hot pan. Tilt the pan to roll the wet batter around the base, making sure it is completely coated in a thin layer.
Cook the crepe for 1 to 2 minutes; when it is ready to be turned, it should slide around easily in the pan. At this point, use a spatula to flip the crepe, and cook it for another 30 seconds. Repeat this process until all of the batter has been used. This should make roughly 8 to 10 crepes, depending on the size of your pan.
Remove the baked pineapple from the oven, and allow it to cool for at least 5 minutes before serving. To serve, fold up 2 crepes, add 2 slices of baked pineapple, and drizzle liberally with the cooled dulce de leche. Serve with whipped cream, a scoop of ice cream, or chopped nuts if desired.