In a stand mixer, fitted with a dough hook attachment, dissolve yeast in warm buttermilk. Let stand 5 minutes, then mix in sugar, oil, eggs, and salt until smooth. Add 3 cups flour, mixing on medium speed until dough pulls away from sides (add additional flour, if dough seems too sticky)
Turn dough onto a floured surface and gently knead in poppyseeds until evenly incorporated into dough. Continue gently kneading until dough is smooth and elastic. Place dough in a greased bowl, turning once to grease top. Let dough rise in a warm place until doubled, about 1-1/2 to 2 hours.
Punch dough down and divide into 12 pieces. Roll each piece into a 15-in long rope. Start twisting each rope around the center until you reach the outside. Pinch edges to seal and tuck underneath.
Place rolls on parchment paper-lined baking sheets and let rise 30 minutes or until doubled.
Bake rolls at 375F 15 minutes or until lightly golden. Cool rolls on a wire cooling rack.
In small bowl, whisk icing ingredients until smooth. Drizzle over cooled rolls and serve.