Preheat oven to 400°F (200°C). Line two baking sheets with parchment paper — one for the churro pieces and one for the bark.
Roll out the puff pastry on a lightly floured surface to smooth any creases. Cut into 1-inch strips, then cut those strips into small bite-sized pieces about 1 inch long.
Arrange the puff pastry pieces on one prepared baking sheet, spacing them 1/2 inch apart. Brush generously with melted butter on all sides.
Mix the sugar and cinnamon in a small bowl. Sprinkle the mixture liberally over the buttered pastry pieces, coating them completely.
Bake for 12-15 minutes until deeply golden brown and puffed, rotating the pan halfway through. The pieces should be crispy throughout. Let cool completely on the baking sheet.
Melt the semi-sweet and milk chocolate together in a double boiler or microwave in 30-second intervals, stirring until smooth and glossy. Let cool for 2-3 minutes.
Pour the melted chocolate onto the second prepared baking sheet and spread into a rectangle about 1/4-inch thick using an offset spatula.
While the chocolate is still tacky but beginning to set (about 3-4 minutes), press the cooled churro pieces gently into the surface, distributing evenly. Sprinkle with sea salt flakes if using.
Let the bark set at room temperature for 1-2 hours until completely firm and snappy. Break into irregular pieces by hand or score and snap into cleaner shapes.
Store in an airtight container with parchment paper between layers at room temperature for up to 10 days.
