Mushroom Barley Risotto

Name: Mushroom Barley Risotto
Ingredients: 1 quart (4 cups) low sodium chicken or vegetable stock; 4 teaspoons olive oil, divided use; ½ yellow onion, finely chopped; 2 cloves garlic, finely chopped; 3 teaspoons chopped fresh thyme, divided use; 1 bay leaf; Kosher salt and black pepper; 1 ½ cups pearl barley; ¾ cup dry white wine; 4 ounces oyster mushrooms, sliced; 4 ounces cremini mushrooms, sliced; 2 packed cups baby spinach; ½ cup freshly grated Pecorino Romano or Parmigiano Reggiano cheese; 1 ounce Neufchâtel cheese (or cream cheese)