Before you do anything else, pull your butter out of the fridge and let it sit out for a bit to soften. It should be very soft.
Bring a large pot of water to a boil over high heat. Once simmering, add at least one tablespoon of Diamond Crystal Kosher Salt to the pot. More than 1 tablespoon is encouraged!
Cook your pasta to al dente according to package instructions, making sure to reserve about 1 cup or so of the pasta cooking water. If using fresh pasta, boil very quickly, then drain and reserve pasta water.
In a large mixing bowl, add the uni (18 or so pieces) and use a whisk to mash the uni Into what looks like an uni purée. Try to get it as smooth as possible before proceeding. If desired, you can use a food processor for this.
Add the softened butter (½ cup or 8 tbsps) to the bowl of uni purée, then use either a whisk or a wooden spoon to mix until completely combined. The final result will be a pale-orange butter mixture, it should not look streaky or liquid-y.
Place the bowl into the fridge or freezer for about 5 minutes just to firm up slightly.
Add the cooked pasta back to the still-warm pot, but removed from the flame. Add about ⅓ of the uni butter into the hot pasta, and stir aggressively to combine and emulsify. Add about ¼ cup of starchy pasta water while combining.
Repeat this process until all of the uni butter has emulsified into an uni sauce, using as much or as little pasta water as necessary.
Add about 1 tablespoon of yuzu juice or lemon juice.
Stir to combine.
Taste and, if necessary, add salt and black pepper to your liking.