For the dough: Place ½ cup of warm apple cider in your electric mixing bowl. Add the yeast and allow it to swell for 5 minutes. It should look foamy. Then add 1 ¼ cups of room-temperature apple cider, plus the oil and salt.
Place a bread hook attachment in an electric mixer. Mix on low, adding the flour a little at a time. “Knead” in the mixer for 3-5 minutes until well combined but tacky.
Oil a large bowl. Place the dough in the bowl and turn it to cover in oil. Cover tightly with plastic wrap and allow the dough to rise for 2 hours.
When to dough is more than double the original size, punch it down and place it on a floured work surface.
Preheat the oven to 400 degrees F. Line two baking sheets with parchment paper. Divide the dough into two equal pieces, to make it easier to work with. Use your hands to turn the edges of the dough under to create a perfectly round, smooth mound.
Roll the dough (from the middle out) into a 12-inch circles. Then using a pizza cutter (or sharp floured knife) cut the dough into strips ¾ X 4 inches long.
Flour you hands and roll each strip into a 6-inch “snake.” Then cross the ends and tie the snake into a loose knot. Place it on a piece of parchment paper and repeat with the rest of the dough. The knots will expand, but not much. You can put them fairly close together.
Bake for 10 minutes. Meanwhile, melt the butter in a large bowl. While the knots are still hot, toss them in the butter—coating each completely.
Place the sugar and cinnamon in a brown paper bag. Using a slotted spoon, scoop the knots out of the butter and place them in the bag. Shake the knots until they covered in cinnamon sugar. Serve warm!