Wash the rice very thoroughly, using several changes of warm water. Continue to rinse until the water runs clear. Soak the rice overnight in cold water to cover, with 1 tablespoon of the sea salt.
Heat a large, heavy skillet over medium heat. Add 2 tablespoons of the olive oil and the onion, cooking until the onion becomes translucent. This should take about 10 minutes.
Add the lentils, garlic, pepper, and paprika and continue cooking for about 2 minutes.
Add 2 cups of water, cover, and continue cooking until the lentils are tender. This should take about 45 minutes. Season with the one teaspoon of sea salt and stir in the basil.
In a large saucepan over medium to medium high heat, bring 2½ quarts of water to a boil with the remaining tablespoon of salt.
Drain the rice from the soaking liquid. Add it to the boiling water and return to a boil, cooking for 10-12 minutes uncovered, stirring occasionally. Test a grain of rice. It should be cooked almost entirely, except for a small part in the center. Strain the rice and rinse with warm water. Drain.
Heat 2 tablespoons of olive oil in a large non-stick stockpot, covered, over medium heat. Add about 2 tablespoons of water and sprinkle the cooked rice evenly onto the bottom of the pot, just a spoonful at a time, until two-thirds of the rice has been distributed.
Take the lentil mixture and spread it evenly over the rice. Cover the lentils with the remaining rice, mounding it in the center.
Use the handle of a wooden spoon to make about 5 holes in the rice from the surface of the rice all the way to the bottom of the pot. These holes are to permit the steam to escape. Now cover the pot with a thick cotton dishtowel and place the lid on tightly.
Reduce the heat to medium-low and cook the lentil and rice mixture for about 35 minutes, turning the pot occasionally.
Fill the kitchen sink with cold water about 2 inches deep.
Remove the cover from the rice and have a large platter ready.
Place the pot in the sink for 1 minute, being careful not to allow any water to enter the pot. Remove the pot. Dry the bottom, then invert the rice cake onto the platter. It should unmold itself in one piece, and it should be golden brown on the bottom.
Serve the dish family style, cutting individual wedges from the rice cake.