Simmer the skate with the aromatics in enough water to cover everything well for about 30 minutes. When the skate is the cooked remove it, drain it, set it on a cutting board and shred it. Strain and reserve the broth, discarding the aromatics.
Meanwhile, in a separate pot, gently sauté the garlic, parsley and anchovy in olive oil until the garlic is just beginning to slightly brown and give off its aroma. Add the tomatoes, crushing them between your fingers as you drop them into the pot. Let simmer until the tomatoes have melted into a saucy consistency.
Add the Romanesco flowerets to the pot, mix them gingerly so they're covered with the tomato sauce. Let everything simmer together for a few minutes, then add the strained skate broth to the pot. Continue simmering for a few minutes more, until the flowerets are nearly tender and you have a rich tasting broth. Taste and adjust for seasoning.
Add the spaghetti pieces and continue simmering. When the spaghetti is cooked, lower the heat and add the shredded skate for a few moments, just long enough to re-heat. (The delicate flesh is liable to fall apart if you let it cook any longer.)
Serve immediately. If you like, reserve a bit of the skate for garnish, along with a sprinkling of minced parsley. A drizzle of best quality of olive oil wouldn't be amiss.