Place the dried porcini in a heatproof bowl and pour the boiling water over them; soak until softened, 20β30 minutes. Rinse the pearl barley in a fine-mesh sieve until the water runs mostly clear; drain.
Heat 2 tablespoons of the olive oil in a large pot over medium-high heat. Add the sliced cremini mushrooms and cook, stirring occasionally, until deeply browned and most liquid has evaporated, 8β10 minutes. Transfer mushrooms to a bowl.
Add the remaining 1 tablespoon olive oil to the pot. Add the chopped onion, diced carrots, and diced celery; season lightly with kosher salt and cook over medium heat, stirring, until softened and translucent, 6β8 minutes.
Stir in the minced garlic and dried thyme and cook until fragrant, about 1 minute.
Return the browned mushrooms to the pot. Add the rinsed barley and cook, stirring, to lightly toast the grains, 1β2 minutes.
Lift the soaked porcini from their liquid; finely chop them. Strain the soaking liquid through a fine sieve or coffee filter to remove grit. Add the chopped porcini, strained soaking liquid, vegetable broth, and bay leaves to the pot. Stir in about 1 teaspoon kosher salt and the black pepper. Bring to a simmer.
Partially cover and simmer gently, stirring occasionally, until the barley is tender but pleasantly chewy and the soup has a rich body, 45β55 minutes. If needed, skim any foam. Taste and season with the remaining kosher salt and more black pepper as needed.
Remove and discard the bay leaves. Stir in the chopped dill. Let the soup rest off heat for 10 minutes to thicken slightly, then ladle into bowls and serve.