Make the dough: Combine flour, sugar, salt, and yeast in a large bowl. Add lukewarm non-dairy milk and melted butter. Mix into a shaggy dough.
Knead with stand mixer and dough hook for 7–8 minutes, or by hand 10–12 minutes, until smooth and tacky but not sticky.
Form dough into a ball, place in a greased bowl seam-side down, cover with plastic wrap, and let rise in a warm place until doubled, 60–90 minutes.
Form the rolls: Mix sugar, cinnamon, and flour for filling. Roll risen dough into a 12x15 inch rectangle. Brush with non-dairy milk, sprinkle filling evenly, leaving 1/2 inch bare edge.
Roll into a log from the short side, seal seam. Cut into 10 pieces using floss or a sharp knife. Arrange in a greased 8x12 inch dish with space between rolls. Cover and refrigerate overnight.
Bake: Next day, let rolls rest at room temp 30 minutes. Preheat oven to 350°F (175°C). Bake 30 minutes until golden, rotating once.
Frost: Whisk powdered sugar, vanilla, and 2–3 tbsp non-dairy milk until smooth. Add extra sugar or milk as needed. Drizzle over warm rolls and serve.
Notes
Use soy or almond milk. Let dough rise in a warm spot—on top of fridge, in a sunny window, or oven proof setting. Overnight fridge rest improves flavor and texture.