Rinse the Brussels sprouts under cold running water and pat dry. Barely trim the bases (these are where the leaves are attached, and the higher you trim, the more leaves you lose), then slice the sprouts in half lengthwise, discarding any loose or wilted leaves.
Coat the bottom of a medium-sized lidded sauté pan generously with olive oil and heat over medium heat until the oil is good and hot. Place sprouts cut side down in the pan and set timer for 5 or 6 minutes. The sprouts will be kind of crowded together and that’s okay.
At 5 or 6 minutes, flip one of the first sprouts you put in the pan. If it has a decent char on it, flip all of them. If not, flip it back and let the sprouts cook a little longer. If it’s nicely cooked, flip the rest and let them cook for another 5 or 6 minutes. The sprouts can get lively at this time—some may flip back. If they seem too charred, don’t despair; see the Kitchen Notes.
Turn off the heat, add the butter in pats to the pan and cover it with a lid. Let it sit for a minute, then stir to coat the sprouts with butter. Season with salt.
Now, optionally, you can grate some Parmesan over the sprouts or top them with some fresh lemon juice. Serve.