Cut the zucchini into fat coins, roughly 1/3-inch thick.
Set a large heavy-bottomed pot over medium heat and add 1⁄4 cup olive oil. Add all the zucchini, a heavy pinch of salt, garlic, and 3 sprigs of basil. Put a lid on the pot and let the zucchini slowly cook, steaming itself out. If you are worried about it drying out and sticking, add a little bit of water. The goal is not to get a lot of color or char, but a little bit is okay. Take care not to stir, as it will start to break.
When the zucchini is uniformly tender, take it off the heat. Remove the basil and discard. Add the cultured butter to the pot and gently stir to integrate it into the soft zucchini. At this point some pieces may fall apart, and that’s okay.
Taste. Does it need more salt? There should be enough acid from the cultured butter, but make sure you used enough butter to give it that rich silky bite.
To serve, scoop into a bowl, drizzle a little olive oil, sprinkle with black pepper, and tear fresh basil sprigs to garnish.