Zest the lemons and juice them into a cup. Finely grate the parmigiano; you will have about 2 handfuls. Bring the water to a simmer in a medium pot. Coat a wide, heavy saucepan with oil (about 2 tablespoons) and warm 3 basil leaves in it over medium heat until fragrant, about 1 minute. Remove the basil leaves and discard them. Add the shallots to the pan, cook them until soft, 2 to 3 minutes, then add the rice. Using a wooden spoon, stir constantly until the grains of rice are glossy and well coated, about 2 minutes. Raise the heat to high and pour in the wine, stirring until evaporated.
Add 2 teaspoons salt to the pot of water. One ladleful at a time, add hot water to the rice, and stir until it’s completely absorbed. Continue adding hot water gradually, only adding more when the rice is ready to absorb it; you will know it’s ready when the bubbling increases and the spoon leaves a slow trail in the rice. Stir after each addition of water and cook until the rice is loose and creamy, and when you bite into a grain of rice it’s barely tender, 18 to 20 minutes (you might have about ½ cup of water left).
To finish, stir in the lemon zest and juice. Pour in a stream of olive oil (about 2 tablespoons), stirring the risotto vigorously at the same time. Stir in the parmigiano; add salt if needed. Tear 2 basil leaves in half and stir them into the risotto. Grind pepper over each serving, and drizzle with olive oil.