Bring a large pot of water to a rolling boil. Salt the water and drop in the pasta. Cook until just under al dente, tender but firm to the bite, stirring occasionally with a wooden spoon. Drain the pasta in a colander, reserving 1/2 cup (120 milliliters) of the pasta cooking water.

Meanwhile, in a medium saucepan over medium heat, combine the oil and garlic and gently sauté until the garlic softens and turns lightly golden. Discard the garlic. Add the monkfish to the pan and sauté for about 1 1/2 minutes, tossing occasionally. Add the wine and bring to a boil. Lower the heat slightly and simmer until the wine reduces by half. Add the tomatoes, fish stock, pepper flakes, and a little salt to the pan and toss occasionally until the tomatoes break down and release their juices and the meat is opaque and cooked through, about 10 to 12 minutes. Using a slotted spoon or wire skimmer, transfer the fish to a bowl, cover, and set aside.

Add the pasta, parsley, and a small ladleful of the pasta cooking water to the pan and toss until the pasta is al dente and well coated with the sauce, about 2 minutes, adding a little more pasta cooking water, if more liquid is needed.

Divide the pasta among the plates and portion the fish on top. Drizzle with a little olive oil and serve immediately garnished with minced parsley.