Stir the ¼ cup sugar into the warm water, sprinkle the yeast on top, and let sit 5 to 10 minutes until foamy.
Cover the raisins with hot water for 10 minutes, then drain and pat dry.
In a large bowl, combine the flour, remaining ¼ cup sugar, salt, and cinnamon. Add the yeast mixture, oil, and egg; stir into a shaggy dough.
Knead on a floured surface 6 to 8 minutes until smooth and elastic.
Place in an oiled bowl, cover, and let rise about 1 hour, until doubled.
Punch down and divide into 4 pieces. Press each into a small rectangle, scatter with raisins, roll up tightly from the short side, and pinch the seam.
Place seam side down in 4 greased 5¾ × 3-inch mini loaf pans. Cover and let rise 45 to 60 minutes, until crowned above the pans.
Preheat the air fryer to 320°F for 5 minutes. Brush the loaves with melted butter.
Air fry 2 pans at a time at 320°F for 10 to 12 minutes, until deep golden and 190°F in the center. Tent loosely with foil for the last 5 minutes if browning too fast.
Cool in the pans 5 minutes, then on a wire rack at least 20 minutes before slicing.