In a large bowl, whisk together the flour, sugar, cocoa powder, baking soda, and salt. Whisk in eggs, water, oil, vanilla, and 1 1/4 cups of the beet purée. Reserve any remaing purée for another use. Pour the batter into the prepared pan. Bake for about 45 minutes, until a toothpick comes out clean. Allow to cool on a wire rack for 20 minutes, then transfer to a dish and allow to cool completely.