Preheat the oven to 200 degrees. Peel the sweet potato, cut it into chunks, and boil them in salted water for twenty minutes until completely soft.
Meanwhile, dry-toast the hazelnuts in a skillet until the skins loosen. Rub them in a clean kitchen towel to remove the bitter skins, then finely chop the nuts. Mix them with some thyme leaves, salt, and pepper.
Pat the cod loin dry, season with salt, and brush the top with the mustard. Firmly press the hazelnut mixture onto it; the mustard acts as a glue while providing the sharpness that rich nuts need. Place the fish on a baking sheet lined with parchment paper, drizzle with a tablespoon of olive oil, and bake in the oven for twelve to fourteen minutes, until the fish is just opaque in the center and flakes easily.
Cut the romanesco into florets and boil them for four minutes until al dente. Heat the remaining olive oil with the crushed garlic in a pan and sauté the florets for two minutes until they get some color here and there.
Drain the sweet potato, let it steam dry for a moment, and mash it with the butter into a coarse puree. Season to taste with salt and pepper. Serve the cod on top of the mash with the romanesco on the side and a lemon wedge.