In a mixing bowl, combine yeast, warm water, and sugar. Mix just until yeast is dissolved. Allow mixture to sit for 5 minutes. After 5 minutes, the yeast mixture should be a bit frothy.
Add salt, milk, butter, eggs, and flour. Mix until dough begins to form one large ball. If your dough is still mushy, add more flour until dough forms one ball.
Coat a bowl in olive oil and place your dough that has been formed into a ball in the bowl. Turn once so that your greased side of the dough faces up. Cover with a damp cloth and allow to rise until it is double in size. You can tell if the dough has doubled by taking two fingers and pressing them into the dough. If it leaves an indent, the dough is doubled in size. This should take about 1 ½ to 2 hours if stored in a place that is draft-free and about 80 to 85°F.
Punch down your dough after it has risen the first time. Lightly flour a clean surface and roll dough out on it. Roll dough into a rectangle shape for larger cinnamon rolls. Brush your melted or soft butter on the dough, then sprinkle with brown sugar and cinnamon. Roll the dough into a loaf shape.
Using a knife or long piece of floss, cut your cinnamon rolls so that they are about 1 ½ inch to 2 inches wide. Place cinnamon rolls in a greased pan, cover, and allow to rise until double in size. This should take between 40 to 60 minutes.
Preheat oven to 350°F. Bake for 20-30 minutes, or until a toothpick inserted in the middle comes out clean. Remove and allow to cool while you create the frosting.
In a mixing bowl, combine powdered sugar, melted butter, vanilla, and milk. Mix until well combined. If your frosting is too runny, add more powdered sugar, if it is too thick, add a little bit more milk. Drizzle on top of cinnamon rolls while they are still warm. Serve right away and enjoy!