Step 1

Make the pasta dough: In a medium bowl, whisk together the egg, yolks and olive oil. In the bowl of a stand mixer fitted with the dough hook attachment, mix together the flour and salt. Add the egg mixture to the flour and knead the dough for 4 to 5 minutes. Transfer the dough to a lightly floured surface, form into a round ball, cover with plastic wrap and let rest for 1 hour.

Step 2

While the dough rests, make the chestnut filling: In a small saucepan, add the chestnuts, 2 cups heavy cream and butter. Bring the mixture to a boil then reduce to a simmer for 15 minutes.

Step 3

Transfer the chestnut mixture to a high-speed blender and blend until smooth while gradually adding the remaining 1 cup of heavy cream. The purée should be thin enough that the blades of the blender don't stick. Season to taste with salt, transfer to a bowl, cover with plastic wrap directly over the purée and allow to cool completely. Transfer the purée to a piping bag and set aside.

Step 4

Divide the pasta dough in half and cover the half not being used with a towel to prevent it from drying out. Roll out the first half of the dough into a sheet that's 20 inches by 8 inches by ⅛ inch. Cut the pasta sheet in half lengthwise and pipe a ½-inch-thick strip of filling lengthwise down the middle of the pasta. Brush the top half of the pasta with the egg wash, then pull the bottom half over the filling and press lightly onto the top half of the strip to seal. Using your fingers, press down on the filled section of the pasta to form 1-inch-long pieces of agnolotti. Make sure that there is no filling in between each pasta indent, then using a fluted piecrust cutter, cut the pieces of agnolotti. Transfer the agnolotti to a lightly floured, parchment-lined sheet pan, sprinkle with flour and set aside.

Step 5

Bring a large pot of salted water to a boil. While the water comes to a boil, make your sauce. In a large sauté pan, heat the olive oil over medium heat. Add the celery and leeks, and sweat for 10 minutes. Add the celeriac and cook until tender, 5 to 7 minutes. Add the celery seeds, milk and heavy cream; bring to a simmer, then reduce to low and cook for 15 minutes.

Step 6

While the milk and cream are reducing, add your pasta to the boiling water and cook until tender, 4 to 5 minutes. Strain the pasta and add the pasta sauce to the pot. Turn off the heat, add the lemon juice, season with salt and pepper, and transfer to a serving dish. Garnish with celery leaves, chervil and shaved black truffles, then serve.