Preheat the oven to 350º. Line an 8 x 8 inch baking pan with parchment paper and butter the sides.
Filling: Add ½ cup of sugar, rhubarb, 1 teaspoon of vanilla, and ¼ cup water to a saucepan. Cook over medium heat until the rhubarb has softened, about 10 minutes. Let it cool completely. Once cooled, drain with a metal sieve to remove excess liquid.
Crumble: Add ½ cup of flour and ¼ cup of sugar to a small bowl. Add the butter to a small saucepan over medium heat and cook until it begins to turn brown. Pour the butter over the flour and sugar mixture and stir with a fork until incorporated. Set aside.
Cake: Cream butter and sugar in a large mixing bowl of an electric mixer until light and fluffy, about 2 minutes. Add the egg and mix until incorporated. Add yogurt and vanilla and mix well. Slowly add the flour and mix just until there is no flour visible. Spread half of the batter in the prepared pan. Place half of the drained rhubarb on the cake batter. Place the rest of the cake batter over the rhubarb. Top with the remaining rhubarb. Sprinkle all of the crumble over the cake and bake for 40-45 minutes until the crumble is golden brown and a toothpick comes out with just a few crumbs.