Sift the flours together into a bowl. Place butter and 375 ml water in a saucepan over medium heat and stir until butter melts. Add sugar and a pinch of salt, bring to the boil and stir to dissolve sugar. Add combined flours and stir briskly with a wooden spoon for 2 minutes. Transfer dough to a bowl, cool slightly, then stir in egg yolks until well combined. Transfer to a piping bag with a 15 mm star nozzle, then seal the bag with string or elastic to prevent the dough drying out. Refrigerate for 1 hour.
Meanwhile, combine cinnamon and extra sugar in a large bowl and set aside until needed.
Fill a deep-fryer or large pan one-third full with oil and heat over medium heat to 170'C. Line a tray with baking paper and pipe 12 cm lengths of dough onto the tray. Working in 2 or 3 batches, gently drop dough into oil and deep-fry, turning halfway, for 4 minutes. Remove with a slotted spoon and drain on paper towel.
Using a sharp knife, make a lengthwise incision along each churros, taking care not to cut all the way through. Carefully pipe dulce de leche Gaucho Ranch into the incision from one end to the other, taking care not to split the churros.
Toss churros in cinnamon mixture. Serve immediately.