Grease a 9x13-inch pan with melted butter; line the bottom with parchment.
Bloom yeast in warm milk with the granulated sugar; let sit until foamy, 5–10 minutes.
Mix softened butter and salt into the milk mixture. Stir in flour gradually until a soft dough forms.
Knead on a lightly floured surface until smooth and elastic, 8–10 minutes.
Place dough in a greased bowl, cover, and let rise in a warm spot until doubled, about 45–60 minutes.
Cook the filling: melt butter in a skillet. Add apples, brown sugar, and cinnamon; cook until tender, 5–7 minutes.
Stir in lemon juice. Sprinkle over cornstarch and cook, stirring, until glossy and thickened, 1–2 minutes. Cool completely.
Beat cream cheese with powdered sugar, 1 tsp vanilla, and a pinch of salt until smooth. Chill while dough rises.
Punch down dough and roll into a 12x18-inch rectangle.
Spread cheesecake mixture over the dough, leaving a 1-inch border. Scatter cooled apples evenly on top.
Roll up tightly from a long side and pinch the seam closed. Slice into 12 equal rolls.
Arrange rolls cut-side up in the pan. Brush tops lightly with melted butter. Cover and rise 20 minutes while preheating to 350°F.
Bake until golden and set in the center, 22–26 minutes. Cool 10 minutes.
Whisk powdered sugar, milk, remaining 0.5 tsp vanilla, and cinnamon until smooth. Drizzle over warm buns and serve.