Add the flour, salt and approximately half of the butter to a food processor, pulse 10-15 times until just combined.
Add the remaining butter, pulse to combine (don’t over-process).
Add the flour mixture to a flat surface, make a well in the center, add the beer.
Mix with your hands until combined (this can also be done in a food processor, just make sure not to over mix or the dough will turn out tough).
Add to a lightly floured surface, roll into a rectangle about ½ inch thick. Fold into thirds, like a letter about to go into an envelope.
Roll again, then fold again. Repeat the process 3-4 times (this is how you get the layers).
Wrap in plastic wrap and chill for at least 2 hours (can be made several days in advance).
Preheat the oven to 425°F.
In a small bowl stir together the brown sugar, white sugar, cinnamon, and salt, set aside.
Roll the puff pastry into a rectangle on a lightly floured surface.
Add the melted butter and beer together (warm again if the beer makes the butter seize a bit) then brush the rectangle with the mixture.
Sprinkle liberally with a little less than half of the cinnamon-sugar mixture, reserve the remaining mixture.
Starting on the long end, roll the puff pastry into a tight log. Slice into 1-inch slices.
Add the slices, cut side up, to a baking sheet covered with a sheet of parchment, press down to flatten the slices.
Brush slices with the beer mixture.
and then sprinkle with a little of the sugar mixture (reserve the remaining cinnamon-sugar mixture).
Bake for 18-20 minutes. Remove from oven and allow to cool enough to handle.
One at a time press curl into the remaining cinnamon-sugar mixture to coat.
Add the ingredients for the chocolate sauce to a microwave-safe bowl. Heat for 30 seconds, stir and repeat until well combined.
Serve the churro curls alongside the chocolate mixture.