Measure out 1/2 cup dried lentils, rinse, and add to 1 1/4 cups of water in a medium sized pan. Bring to a boil, then reduce to simmer and cover.
Simmer for approximately 20 minutes, or until most of the water is absorbed, and the lentils are tender but not yet broken apart. Drain in a colander.
Using a large food processor, blender or potato masher, briefly pulverize the drained lentils until they form a purée – they should be the consistency of pumpkin purée. Add water by the tablespoon if it is too dry; it will set up as it cools, so don’t add water unless you need to do so.
Measure out 1/2 cup of purée for the recipe, cover and place the purée in the refrigerator while you prepare the rest of the recipe.
Preheat oven to 350° F (static) or 325° F (convection).
Oil an 8-inch round pan, then line with parchment paper (oiling the bottom of the pan first helps to keep the parchment in place; the parchment helps you get the cake out easily!).
Whisk together the dry ingredients in a large bowl. Beat the sour cream, eggs, vinegar, vanilla and cooled lentil purée together, then add in with the dry ingredients. Slowly pour in the hot water while beating the other ingredients together. The batter will be fairly thin, but should not be watery. Add less water if you think your batter is getting too thin.
Pour batter into the prepared pan and smooth with a rubber spatula.
Bake for 25 minutes, or until a cake tester or toothpick inserted into the center comes out clean. Remove to cool on a wire rack for 10-15 minutes, then remove the cake by lifting up on the parchment.
To serve, dust the tops of each piece with powdered sugar.