The kelp pasta is the key to this dish; yes, you can of course make it with regular pasta, but then it's not so special, is it? But believe it or not, you can buy kelp powder online or in health food stores. I made my own, but I guess I didn't need to. Everything else in this recipe is up to you.
Start by making the pasta. Mix all the ingredients well in a large bowl and form into a dough. Knead it for 4 to 8 minutes, until the dough becomes elastic and pliable. Cover the dough with plastic wrap and let it rest for 1 hour. Or, if you have a vacuum sealer, you can vacuum seal the dough and it will hydrate instantly. Chef's trick.
Either way, you'll need to let the "sauce" marinate. Mix all the ingredients for the fish except for the lemon juice and bottarga together in a bowl. Cover and let this marinate at room temperature for at least 30 minutes, but I normally let it marinate all during the time it takes me to roll out my pasta.
Roll the pasta out on an Atlas pasta maker, or whichever pasta roller you have (or roll by hand) until the dough is thin but not too thin. I go to No. 7 on my Atlas, which is two stops before the thinnest setting. Either cut your tagliatelle by hand or use the Atlas linguini attachment to cut your noodles. Dust the freshly cut pasta with some flour and set it on a baking sheet that is either lined with parchment paper or that has been sprinkled with semolina flour or cornmeal.
To finish the dish, boil the pasta until it floats, and then for 1 more minute. Drain and toss with the sauce. Add the chopped herbs, lemon juice to taste and then grate the bottarga over it if you are using it. Serve with a crisp white wine; I'd suggest a Sancerre or a really good Pinot Grigio.
Notes
Once you make the pasta, it will dry reasonably well (it gets brittle, though) so if you wanted to dry it fully you can.