In a large mixing bowl, dissolve the yeast and 1 tablespoon of the granulated sugar in the warm milk. Let it sit for 5-10 minutes until foamy.
To the yeast mixture, add the remaining granulated sugar, melted butter, eggs, vanilla extract, salt, and 4 cups of flour. Stir with a wooden spoon until a shaggy dough forms.
Turn the dough onto a lightly floured surface and knead for 5-7 minutes, adding the remaining 1/2 to 1 cup of flour as needed to prevent sticking, until the dough is smooth, elastic, and springs back when lightly pressed.
Place the dough in a greased bowl, cover with a clean kitchen towel, and let rise in a warm place for 1 to 1 1/2 hours, or until doubled in size.
Punch down the risen dough and roll it out on a floured surface into a 16x20-inch rectangle. Spread the softened butter evenly over the surface, then sprinkle evenly with the brown sugar and cinnamon.
Starting from a long side, tightly roll the dough into a log. Use a sharp serrated knife to cut the log into 18 equal slices. To shape hearts, gently pinch the bottom of each round roll to form a point, then use two fingers to press and create an indent at the top.
Arrange the shaped rolls, with the pinched points touching, in two concentric circles on a parchment-lined baking sheet to form one large heart. Cover lightly and let rise for 30-45 minutes until puffy.
While the rolls rise, preheat oven to 375°F. Bake the risen rolls for 20-25 minutes, until golden brown. Cool slightly before whisking together the icing ingredients and drizzling over the warm rolls.