Melt butter in a large cast iron skillet or Dutch oven over medium-low heat. Add sugar and rhubarb; cook until rhubarb is soft, 5 to 8 minutes. Remove from heat.
Mix gluten-free flour, baking soda, and salt together in a large bowl. Add yogurt, coconut oil, egg, and vanilla extract; stir thoroughly until batter is combined.
Drop cake batter over rhubarb mixture in the skillet. Spread it out gently until mostly smooth.
Bake in the preheated oven until top is golden and a toothpick inserted into the center comes out clean, about 25 minutes.
Run a knife around the edges, place a plate on top and carefully invert cake onto the plate.
