Heat the oven to 400°F with a rack in the middle. Set out a 5-quart Dutch oven or another deep ovenproof pot with a lid.

Put the olive oil into the Dutch oven and warm it over medium heat.

Add the chopped onion to the pot with 1/2 teaspoon of the kosher salt. Cook for 4 to 5 minutes, stirring a few times, until the onion softens and looks glossy.

Add the sliced mushrooms to the pot. Cook for 8 to 10 minutes, stirring now and then, until they give off their liquid and then start to brown.

Add the sliced garlic and dried thyme to the pot. Cook for 1 minute, stirring, until the garlic smells fragrant.

Add the rinsed pearl barley to the pot. Stir for about 1 minute so the grains get coated in the oil and pick up some of the mushroom flavor.

Add the drained cannellini beans, the vegetable broth, the remaining 3/4 teaspoon kosher salt, and 1/2 teaspoon of the black pepper to the pot.

Raise the heat to medium-high and bring the mixture to a full boil. Stir once so no barley is stuck on the bottom.

Cover the pot with its lid and transfer it to the oven. Bake for 35 minutes.

Take the pot out of the oven and remove the lid carefully. Stir the barley from the bottom to the top.

Check a spoonful of barley. It should look plump and be almost tender, with just a little firmness in the center; if it is still quite hard, cover the pot and bake 5 minutes more.

Add the baby spinach to the pot in a few handfuls. Stir after each handful until the spinach wilts into the hot barley.