In the bowl of a stand mixer, combine all of the ingredients and mix on medium-low speed for 7 minutes, or until the dough comes together in a smooth ball.

Remove the dough and knead it with your hands for 3 minutes. The dough should be slightly tacky but not sticky.

Wrap the dough tightly with plastic wrap and chill in the refrigerator for 30 minutes.

Cut the dough into 4 equal portions, set 1 aside, and cover the remaining 3 with a towel or plastic wrap until you are ready to use them.

Using a rolling pin, flatten the portion you set aside into a 6×4-inch square. If the dough feels sticky, you can dust it with a little semolina flour.

Feed the dough through a pasta sheet roller on setting No. 1 on low speed. Then fold the dough over, turn it so the wide side is first, and feed it through again. Repeat 6 times total. The dough will begin to get slightly lighter in color and feel a bit softer. Note: you want your pasta sheet to be about the width of the sheeter, so keep turning it as needed.

Turn the machine to setting No. 2 and feed the dough through 3 to 4 times. At this point the dough should feel very smooth; if it feels tacky, dust it with a little semolina flour.

Continue sheeting the pasta, moving the machine to settings No. 3, No. 4 and No. 5, and feeding the dough through 3 to 4 times per setting. (For a thicker, more hearty pasta, stop after the No. 5 setting. Use No. 6 for a slightly thinner pasta and No. 7 for very thin pasta.)

Lay the dough sheet on a clean work surface dusted with a little semolina flour. Dust the top of the sheet with a little more semolina flour and roll it up, starting on the short side and keeping it straight and tight without applying too much pressure.

Using a knife, cut the roll into ½-inch thick slices. Unravel the noodles, lay them in a line and then twist them into a nest. Transfer the nest to a sheet pan dusted with a little semolina flour.

Repeat steps 5 to 10 for the remaining dough portions.

Cook the pasta immediately (see instructions below) or freeze the nests directly on the sheet pan, then transfer them to plastic bags and store in the freezer for up to a month.

In a medium saucepan over medium-low heat, warm the olive oil for 2 minutes, then add the garlic and anchovies and cook for 2 to 3 minutes, stirring frequently, until the garlic is lightly browned and fragrant.

Add the crushed red pepper and cook for 1 minute, stirring frequently.

Add the olives and capers and cook for 1 minute.

Add the tomatoes and break them up into bite-sized pieces with a wooden spoon. Bring the sauce to a simmer and then reduce the heat to low and cook for 30 minutes. Season with kosher salt and black pepper to taste.

Meanwhile, bring a large pot of salted water to a boil and cook the fresh pasta until al dente, 4 to 6 minutes.

Strain the pasta and divide between 4 bowls. Top with a generous amount of sauce and garnish with the fresh herbs and Parmesan. Serve hot.