There's a lot of debate about whether morels should be rinsed under water, dry-brushed with a paper towel, or soaked in salted water remove the grit. We opt for a middle ground and rinse them quickly under cool running water. We use an old soft-bristled toothbrush to gently scrub between the folds and then pat them dry with a paper towel.
Morels have a hollow center and the larger mushrooms can sometimes collect dirt (or the occasional insect traveler) inside. In these cases, we slice the morels in half before cleaning. The presentation isn't quite as striking, but we'll compromise in order to avoid sandy mushrooms.
Both the cone-shaped body and the stem are edible. We trim the end of the stem if it's particularly woody or dried out.
Don't wash morels until right before you're going to cook them. Freshly picked and refrigerated in a paper bag, they'll actually keep for several days, but their quality deteriorates rapidly once they've been washed.
What's your favorite way to eat morels?
Related: Tip: Save Mushroom Stems for Soups!