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1
Separate out 4 of the best-looking pieces of sea urchin roe to be used as garnish, and place the rest of the roe in the pitcher of a blender or bowl of a food processor fitted with the blade attachment. Puree the sea urchin on medium speed for 1 minute, and pass it through a fine sieve, into a bowl. Return the puree to the blender or food processor, using a spatula to make sure you don't leave any of it behind. Add the butter to the blender or food processor and puree until the mixture is smooth.
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2
Bring a medium pot of heavily-salted water to a boil. While the water heats, get set up to finish the dish and plate it: Put 2 tablespoons of water into a small, heavy bottomed pot. Have your sea urchin butter, salt, pepper and a whisk close at hand. Place the chives in a mixing bowl large enough to comfortably hold all of the spaghetti (you'll be tossing the spaghetti and sauce in this bowl).
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3
Once the water is boiling, add the spaghetti and cook it until just al dente.
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4
While the spaghetti is cooking, finish the sea urchin sauce. Bring the 2 tablespoons water to boil in the small pot-this will happen very quickly-then gently whisk in the sea urchin butter. Taste the mixture and season it with salt and Esplette pepper. If the spaghetti is still cooking, cover the sauce to keep it warm.
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5
Once the spaghetti is done, drain it. Add the warm sea urchin sauce and the cheese to the bowl with the chives; mix gently and season with salt and white pepper to taste, then, using tongs, gently toss the pasta into the sauce, making sure it is evenly coated.
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6
Divide the pasta into four serving bowls. Drizzle a tablespoon of the extra sauce from the pasta around each mound. Squeeze lemon juice over each serving, and place one reserved lobe of sea urchin roe and 1 1/2 teaspoons of caviar on top of each mound of pasta. Serve immediately.
