Add the warm water, light brown sugar, and yeast to a large bowl. Set aside for 5 minutes, or until the yeast has bloomed and is foamy on top.
Next add the butter, egg, and vanilla. Mix to combine. Add the flour and gently mix the dough until it forms a shaggy ball.
Transfer the dough to a lightly floured surface and knead the dough for 3-5 minutes, or until it is smooth and bounces back when lightly poked.
Transfer the dough to a lightly oiled bowl and set it in a warm place to rise until doubled in size (about 90 minutes).
While the dough rises, prepare the filling (below).
When the dough has risen, turn it out onto a lightly floured surface and roll it into a ¼” thick rectangle (approximately 15” long and 12” wide).
Spread the orange-cinnamon filling over the dough and roll it tightly into a log. Pinch the seam together to seal the log shut. Slice the log into 1” thick rounds.
Grease a 9x13 pan with butter or nonstick baking spray or line it with parchment paper.
Place the cinnamon rolls in the pan cut side up and press them down slightly until they are 1” tall.
Set the pan in a warm place to rise for 20 minutes while you preheat the oven. While the rolls rise, preheat the oven to 350F.
When the oven is ready, bake the rolls for 30-35 minutes, or until they are golden brown.
Allow the cinnamon rolls to cool slightly while you make the frosting (below).