Heat olive oil in a large heavy-bottomed Dutch oven over medium high.

Add shallots and thinly sliced garlic, and season with salt and pepper. Cook, stirring occasionally, until the shallots are softened and caramelized, about 15 to 20 minutes.

Add red-pepper flakes and anchovies. Stir to melt the anchovies into the shallots, about 2 minutes.

Add tomato paste and season with salt and pepper. Cook, stirring constantly, until the tomato paste has caramelized at the edges and changed to a deeper brick red color, about 2 minutes.

Remove from heat and transfer about half the mixture to a resealable container.

Cook pasta according to package instructions in a large pot of salted boiling water until very al dente.

Transfer the pasta to the Dutch oven with the remaining shallot mixture and 1 cup pasta water. Cook over medium-high heat, swirling the skillet to coat each piece of pasta, until the pasta is thick and sauce has reduced, about 3 to 5 minutes.

In a small bowl, combine parsley and finely chopped garlic clove, and season with flaky salt and pepper.

Divide pasta among bowls or transfer to one large serving bowl, and top with parsley mixture and more red-pepper flakes if desired.