Make the dough: In a large bowl (or stand mixer bowl), combine warmed apple cider and yeast. Let stand 5 minutes until foamy (skip the wait for instant yeast).
Add sugar, melted butter, eggs, and salt. Mix in flour until a soft dough forms. Knead 6–8 minutes (or 4–5 minutes with a dough hook) until smooth and elastic. If sticky, add flour 1 tablespoon at a time.
Place dough in a lightly greased bowl, cover, and let rise in a warm spot until doubled, about 45 minutes.
Cook the apple filling: In a small saucepan, melt 2 tablespoons butter. Stir in diced apples, 1/2 cup brown sugar, apple pie spice, and water. Simmer 5–7 minutes until apples begin to soften.
Stir cornstarch into 1 tablespoon cool water (optional) and add to the pan, or sprinkle cornstarch in while stirring. Cook 1–2 minutes until thickened. Transfer to a bowl and cool; drain off excess liquid so the rolls don’t get soggy.
Grease a 9x13-inch baking pan. On a floured surface, roll dough into a 12x16-inch rectangle, about 1/4-inch thick.
Spread the softened (or melted) butter over the dough. Mix 1/2 cup brown sugar with cinnamon and sprinkle evenly over the buttered dough.
Evenly scatter the cooled apple filling over the cinnamon-sugar layer. Starting from a long edge, roll the dough tightly into a log.
Cut into 12 rolls using a sharp knife or dental floss. Arrange cut-side up in the prepared pan. Cover and let rise until puffy, about 30 minutes.
Preheat oven to 375°F (190°C). Bake 25–30 minutes, until golden and the centers are set (about 190°F/88°C internal temperature if you check).
Make the frosting: Beat cream cheese and 1/4 cup butter until smooth. Mix in powdered sugar, then add cream and vanilla until fluffy and spreadable.
Cool rolls 5 minutes, then spread or drizzle frosting over warm rolls. Serve immediately.