Cover dried porcini with boiling water in a heatproof bowl and soak for 20 minutes. Lift mushrooms out, rinse away any grit and chop finely; strain soaking liquid through a damp paper coffee filter set in a sieve, reserving the filtered liquid.
Heat 2 tablespoons oil in a soup pot over medium-low heat. Add onions and 1/2 teaspoon salt and cook for 35 to 40 minutes, stirring often, until deeply golden and soft.
Meanwhile, heat remaining oil in a large skillet over medium-high heat. Brown fresh mushrooms in 2 batches for 5 to 6 minutes per batch, leaving them undisturbed briefly between turns.
Stir garlic into caramelized onions for 30 seconds, then add sherry and simmer for 1 minute. Add chopped porcini, filtered soaking liquid, broth, thyme, browned mushrooms and remaining salt.
Simmer for 10 minutes, then add kale and pepper and simmer for 7 to 8 minutes until kale is tender. Stir in vinegar and divide among 6 bowls.