For the cake:
Heat oven to 350°F. Butter and dust a round springform cake pan.
Wash and trim rhubarb. Cut half into small cherry-sized pieces, and sprinkle with 1⁄2 cup of sugar. Allow to macerate for half an hour to release some juice. Roughly chop the remaining rhubarb, and cook with the released juice until it is smooth and has thickened. Set aside and let cool.
In a large mixing bowl, cream butter, and gradually add sugar and eggs. Beat in the beets, yogurt, ginger, vanilla, rhubarb, and macerated rhubarb. Sift all dry ingredients in a separate bowl, and fold into wet ingredients, mixing until fully incorporated. Add pecans and stir just to mix through.
Spread batter out evenly and bake for approximately 1 hour, or when a toothpick inserted into the centre comes out clean. Remove from oven, cool on rack until completely chilled, then slice horizontally into two layers. Ice with Ginger Cream Cheese Icing*.
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