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 to prevent any scorching, until the tomato paste has caramelized a bit, 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 to Dutch oven with remaining shallot mixture and 1 cup pasta water. Cook over medium-high heat, swirling to coat each piece of pasta until sauce has reduced, about 3 to 5 minutes.

In a small bowl, combine parsley and finely chopped garlic clove, season with flaky salt and pepper. Divide pasta among bowls and top with parsley mixture and more red-pepper flakes, if desired.