Bring all ingredients together in a food processor, then turn onto a floured surface and knead for 10 minutes until a smooth dough is formed. Wrap in plastic wrap or put in a ziplock bag; let rest for at least 2 hours before rolling dough.

In a heavy-bottomed saucepan, sweat shallots and garlic in butter. Add sunchokes and cook until soft and tender, about 10 minutes. Whisk in heavy cream and vegetable stock, and simmer for 10–15 minutes, until reduced by half.

Use an immersion blender to puree mixture, or transfer to a blender and blend until smooth. Season to taste. Divide the puree: Cover half of the puree and chill until ready for plating. For the pasta filling, in a small bowl, mix half of the puree with the parmesan and mascarpone.

In food processor, combine walnuts, garlic, chile flakes, lemon zest, and olive oil; blend to form a coarse paste. Add arugula and vegetable oil; process until smooth. Salt to taste, transfer to a bowl, and cover until ready to use.

First, prepare the dough. To roll out by hand, place the dough on a large, lightly floured surface, and use a rolling pin to create a very thin sheet, around 1/16 inch thick. A pasta machine makes a consistent, thin sheet.

Next, cut the dough. Using a pasta cutter or sharp knife, cut dough into long rectangles, about 3–4 inches wide, depending on how big you want your agnolotti. Spoon small amounts of the sunchoke filling onto each sheet, spacing the spoonfuls of filling about 1–1 1/2 inches apart. Be careful not to overfill.

To form the agnolotti, fold the dough over the filling and gently press the long edge to seal, making sure there’s no air inside. If desired, use a fork to crimp the sealed edge. Then pinch alongside the filling, pressing to seal each section. Cut through each section with a pasta wheel or knife, trimming any excess dough to make a neat edge, and use your fingers or a fork to crimp the edges.

Bring reserved puree to room temperature. In a stockpot, bring salted water to a boil.

While waiting for water to boil, arrange reserved puree on the side of the plate and give it a swoosh motion to create a well.

When the water reaches a boil, add the agnolotti and boil for 2–3 minutes, or until they float to the surface and are tender. Use a slotted spoon to remove agnolotti from stockpot, and immediately toss with enough pesto to coat.

Plate the agnolotti on the prepared plates along the puree, and top with some more pesto, as you like. I like to garnish with toasted walnuts, some whole fresh arugula or watercress, a spritz of lemon juice, some shaved parmesan cheese, and olive oil.