For the Capellini pasta dough
Combine the flour, egg yolk, whole egg, olive oil, and milk in an electric stand-mixer fitted with a dough hook.
Once the flour is well incorporated, transfer to a clean surface and knead by hand for 1 minute.
Wrap the dough in plastic wrap and let it rest for one hour in refrigerator.
On a lightly floured work surface, roll the dough very thin and cut dough into capellini--or similar shape- -with a pasta roller.
Extra dough can be rolled and frozen for a later use.
For the Capellini pasta sauce
Bring 3 quarts of salted water to a boil and add the pasta.
Cook about 2 minutes (depending on the shape and size of your pasta) or until the pasta is floating and is tender to the bite.
Strain the pasta and return it to the pot along with about 2 tablespoons of the pasta water.
Add the butter and crème fraiche and stir gently to combine.
Season lightly with salt and piment d’Espelette, remembering the caviar will add saltiness as well.
Once the pasta is well coated and seasoned, add Meyer lemon juice, 1 tablespoon of the chives and 1/3 of the caviar, stirring to disperse evenly.
To serve the capellini pasta
Divide the pasta into warmed pasta bowls and top each portion with the remaining caviar, chive and lemon zest.
Use extra piment d’espelette as desired for your taste. Serve immediately.