They say you can't have your cake and eat it, too. But when it comes to some either/ors, you really can. Take covered versus open pots: You can have the lid on, off, or both. Often, that third option is as simple as cracking the lid, but I'm also a big fan of the parchment paper lid, which provides just enough cover, but not too much, for whatever you're cooking.
Why would you want to partially cover a pot? At the risk of stating the obvious, it's to get some of the benefits of both lid-on and lid-off cooking. With a lid fully on a pot, most of the steam released by the food is trapped in the vessel. This hinders browning, as the temperature-limiting effects of water dripping back onto the surface of the stew can seriously slow down that process. And, because the steam condenses on the lid and then drips back down onto the food, it also prevents liquids from evaporating and reducing. With a pot completely uncovered, on the other hand, browning can occur more rapidly on any foods that aren't submerged in the liquids, and the steam can escape, allowing those liquids to cook down.
In a situation like a stew or a braise, though, we want some browning and evaporation for flavor development—just not too much too soon. That's where the cracked-lid and parchment paper–lid options come in: They provide a partial barrier to the steam's escape without fully blocking it.
Choosing between the cracked-lid technique and the parchment paper one comes down to a few considerations. A lid, if your pot has one, is the easier of the two, requiring no work. It's as simple as setting the lid onto the pot, somewhat askew. But I've always struggled with just how cracked a lid should be, and sometimes I find that it bounces between being too effective of a cover when just slightly cracked, and not effective enough when the crack is widened just a little more.
A parchment paper lid, on the other hand, takes a minute or two to prepare. But once ready, it does an admirable job of providing a semipermeable cover for all the food in the pot. It's also incredibly easy to make. Here's how:
Start by cutting a square piece of parchment paper that's just slightly larger than the pot itself.
Fold that square in half, and then in half again. You'll have a quarter-size square with two edges that are open and two that are closed. Now fold this smaller square in half on the diagonal to form a triangle, keeping the closed sides together, and then fold that triangle in half lengthwise a couple more times to form a narrow wedge; with each fold, make sure that the closed sides stay together.
Hold the wedge up to the pot so that its point is right at the pot's center, then use scissors to trim the wedge so that it just fits inside the pot's edge. In math terms, you want the wedge's length to match the radius of the inside of the pot. (If it's a tiny bit smaller, that's fine, but larger won't work, since the paper lid won't fit inside the pot.)
Next, snip off the tip of the wedge. This will create a center vent on the unfolded lid.
Now unfold the lid and confirm that it fits just inside the pot. If it's too big, trim around its edge a little more until it does.
When you're ready to cover your pot, simply press the paper lid directly onto the surface of that food. Most of the parchment paper we home cooks use comes in a roll, so the lid will have a tendency to curl up on itself, which can be a problem if it curls up off the food. To prevent that, make sure to position the paper lid so that it curls downward toward the food.
You can lift the lid off using tongs at any point to check the progress of your stew or braise, then reset it to continue the cooking (or remove it if the food is nearly done and you want a little more browning and evaporation during the last few minutes). When you're done, just toss it—you can have your parchment paper lid, but you can't reuse it. That'd be gross.