Activate the yeast. Warm the milk until it’s like a warm bath (about 110°F/43°C). Stir in the sugar and yeast.
Let it sit 5–10 minutes until foamy. If it doesn’t foam, start over with fresh yeast.
Make the dough. In a large bowl, whisk eggs, melted butter, vanilla, and salt. Add the foamy yeast mixture.
Stir in 3 cups of flour. Mix until a shaggy dough forms, then add more flour 1–2 tablespoons at a time until the dough is soft and slightly tacky but not sticky.
Knead. Knead on a lightly floured surface for 6–8 minutes, or use a stand mixer with a dough hook for 5–6 minutes. The dough should be smooth and elastic.
Shape into a ball.
First rise. Place the dough in a lightly greased bowl, cover, and let it rise in a warm spot until doubled in size, about 60–90 minutes.
Make the apple filling. While the dough rises, melt butter in a skillet over medium heat. Add apples, brown sugar, cinnamon, nutmeg, salt, and lemon juice. Cook 6–8 minutes until tender but not mushy.
If juicy, stir in cornstarch and cook 1 more minute to thicken. Cool completely.
Mix the cinnamon sugar. Combine brown sugar and cinnamon in a small bowl. Set aside the softened butter for spreading.
Roll the dough. Punch down the risen dough and roll it into a 12x16-inch rectangle.
Spread the softened butter evenly. Sprinkle the cinnamon sugar over the butter.
Add the apples. Scatter the cooled apples evenly, leaving a 1/2-inch border on the long edge farthest from you. Press them gently into the dough so they stay put.
Roll it up. Starting from the long side closest to you, roll the dough into a tight log.
Pinch the seam to seal. Trim the ends if needed.
Slice the rolls. Use a sharp knife or dental floss to cut 12 equal rolls. Place them in a greased 9x13-inch pan, leaving slight space between each.
Second rise. Cover and let the rolls rise again until puffy, 30–45 minutes.
Preheat the oven to 350°F (175°C) during this time.
Bake. Bake for 22–28 minutes, until lightly golden and the centers read about 190°F (88°C). If tops brown too fast, tent loosely with foil.
Make the glaze. Beat cream cheese until smooth. Add powdered sugar, vanilla, salt, and 2 tablespoons of milk.
Mix until creamy, adding more milk for a pourable consistency.
Glaze and serve. Spread the glaze over warm rolls so it melts into the swirls. Serve warm and enjoy that apple pie aroma.