How to Make It
Combine apple cider and brown sugar in a small saucepan. Bring to a boil over medium-high, stirring often, until sugar is dissolved. Reduce heat to medium, and cook, stirring often, until liquid reduces by about half, about 10 minutes. Remove from heat, and stir in rose water. Let cool completely. (Syrup will continue to thicken as it cools.)
Combine yeast, 1 teaspoon granulated sugar, and 3/4 cup warm water in bowl of a stand mixer fitted with the paddle attachment, and let stand until bubbling and frothy, about 5 minutes.
Meanwhile, whisk together flour, salt, cinnamon, and remaining 1/3 cup granulated sugar in a medium bowl. Add egg yolks, milk, and vanilla to yeast mixture; beat on low speed until combined. With mixer running on low speed, add flour mixture, beating until dough comes together, about 2 minutes (dough will be very wet).
Cover bowl with plastic wrap or a clean kitchen towel, and let stand in a warm place until doubled in size, about 1 hour and 30 minutes.
Line a large plate with paper towels. Pour oil into a medium saucepan to a depth of 1 1/2 inches. Heat over medium until a deep-fry thermometer reads 350°F. Working in batches of 5 or 6, pinch off walnut-size pieces of dough. Using flour-coated hands, roll each into a rough ball, and drop into hot oil. Fry until golden and cooked through, 2 to 4 minutes per batch, flipping halfway through. Using a slotted spoon, transfer to prepared plate to drain briefly.
Drizzle a generous amount of cooled syrup over hot bimuelos, and serve immediately.