Mix warm water and yeast packet from bread mix together in a bowl and let stand until foamy, about 5 minutes.
Place bread flour mix in the bowl of a stand mixer and add eggs, vegetable oil, vinegar, and yeast mixture; mix using the stand mixer set to low speed until smooth. Turn speed to medium and beat until mixture thickens, about 15 seconds. Transfer dough to a greased bowl, cover bowl with a dish, and allow dough to rise in a warm place for 45 minutes.
Preheat oven to 350 degrees F (175 degrees C).
Spread dough onto a piece of plastic wrap. Brush melted butter over dough and sprinkle white sugar and cinnamon over dough.
Roll dough into a jelly roll-type loaf by lifting 1 end of the plastic wrap and forming dough into roll. Place roll into a glass baking dish. Cut 1/2- to 1-inch slits into the loaf. Pour cream over the loaf.
Bake in the preheated oven until dough is cooked through, 20 to 30 minutes. Break rolls apart.
Mix confectioners' sugar and milk together in a bowl until glaze is smooth; drizzle over warm rolls.