In a large mixing bowl, combine 2 cups of all-purpose flour, granulated sugar, instant yeast, and salt. Heat 1 cup of whole milk with 1/2 cup of unsalted butter until melted, then let cool slightly. Mix in the warm milk mixture along with 2 large eggs, stirring until well combined. Gradually add remaining flour until a soft, slightly sticky dough forms.

Turn dough onto a floured surface, and knead for about 5 minutes until smooth and elastic. Place dough in a greased bowl, cover with a towel, and let rise in a warm place for about 1 hour, or until doubled in size.

After rising, punch dough down gently and roll into a rectangle approximately 1/4 inch thick. Spread 1/4 cup of softened butter over the dough, then sprinkle with a mixture of 1 cup of brown sugar and 2 tablespoons of ground cinnamon. Roll the dough tightly from the long side and cut into 12 to 15 equal pieces.

Place the cut rolls into a greased baking dish, ensuring they are close but not overcrowded. Cover and allow to rise for 30-45 minutes until puffed up.

Preheat oven to 375°F (190°C) while rolls finish second rise. Bake for 20-30 minutes until golden brown and cooked through.

While rolls are baking, whisk together 2 cups of powdered sugar, 1 teaspoon of vanilla extract, and 2-3 tablespoons of milk until smooth. Adjust consistency by adding more milk if necessary.

Once rolls are out of the oven, drizzle frosting generously over warm rolls, allowing it to melt into the crevices. Serve immediately.