Grease a 9x13-inch pan. Warm buttermilk to 105–110°F.
Whisk warm buttermilk and sugar in a large bowl. Sprinkle yeast over.
Rest until foamy, 5–10 minutes.
Stir in melted butter and 2 cups flour until shaggy.
Add salt. Mix in remaining flour gradually to form a tacky dough.
Knead 8–10 minutes on a lightly floured surface until smooth and elastic.
Place dough in a greased bowl. Cover and let double, 60–90 minutes.
Combine softened butter, brown sugar, cinnamon, and salt into a paste.
Punch down dough. Roll into a 12x16-inch rectangle, long side facing you.
Spread filling evenly, leaving a 1/2-inch bare strip along the far edge.
Roll up tightly into a log. Pinch the seam to seal.
Slice into 12 rolls with floss or a sharp knife. Arrange in the pan.
Cover and let rise until puffy, 30–45 minutes. Preheat oven to 350°F.
Bake 22–26 minutes, until lightly golden and set in the center.
Beat cream cheese, powdered sugar, butter, vanilla, and buttermilk until smooth.
Spread icing over warm rolls. Serve.