Combine sugar and yeast for dough in a small bowl.
Mix 1 3/4 cups flour, baking powder, xanthan gum, baking soda, and salt together in a second bowl.
Place milk and butter in a microwave-safe bowl and microwave on high, stirring every 15 seconds, until 110 to 115 degrees F (43 to 46 degrees C), about 45 seconds.
Whisk into the yeast mixture and set aside to proof, about 5 minutes
Combine proofed yeast with olive oil, egg, and vanilla extract in a large bowl; mix for a moment and then slowly add in the flour mixture.
Mix with an electric mixer on medium-high speed until dough thickens and loses some of its stickiness, about 1 1/2 minutes.;
Cover a work surface with a sheet of good quality plastic wrap and a light layer of flour.
Place dough in the center and cover with a little more flour and another sheet of plastic wrap.
Roll out to a 10×13-inch rectangle; remove top layer of plastic wrap.
Combine brown sugar and cinnamon for filling in a small bowl. Spread melted butter over the entire dough rectangle and sprinkle brown sugar mixture evenly over top.
Start at a long edge and roll the dough, using the plastic wrap to help lift and roll as you go
Lightly sprinkle dough with more flour and cut into 10 pieces with a sharp knife.
Place rolls in a greased baking pan, cover with plastic wrap,and place in a warm spot to rise for 15 minutes.
Meanwhile, preheat the oven to 350 degrees F (175 degrees C)
Bake rolls in the preheated oven until tops are golden brown, 22 to 27 minutes.
While rolls are baking, beat butter and cream cheese for frosting in a mixing bowl until smooth.
Add powdered sugar; mix until smooth. Mix in vanilla extract, and salt
Remove cinnamon rolls from the oven and immediately drizzle frosting over top