In a large bowl, combine sugar, vegetable oil, greek yogurt and vanilla. Mix well
Add in dry ingredients and mix until well combined.
Pour into a greased 9x13 pan. Bake 45 minutes or until toothpick inserted into the center comes out clear. Remove from oven and let cool for 30 minutes before cutting.
For the frosting:
Melt butter in a saucepan over medium heat.
Stir in sugar and milk, and bring to a boil, stirring.
Allow the mixture to boil for one minute, stirring the entire time. Remove from heat.
Stir in milk chocolate chips and marshmallows until melted.
Stir in vanilla.
Quickly pour over brownies (or spread if it gets too thick).