Put the porcini and shiitake mushrooms in a medium heatproof bowl. Pour in 2 cups boiling water and weight down the mushrooms with a small plate so they are submerged. Soak until they're plumped and softened, about 20 min. Use a slotted spoon to transfer the mushrooms to a cutting board, squeezing any excess liquid from the mushrooms back into the soaking liquid. Let cool. Remove and discard any tough stems. Coarsely chop the mushrooms. Strain the soaking liquid through a coffee filter or paper towel set in a sieve and reserve.
In a medium (3-quart) saucepan over medium heat, heat the chicken broth with all the mushroom soaking liquid. In another medium saucepan over medium heat, melt the butter. Add the onion and a sprinkling of salt, and cook, stirring occasionally, until soft and lightly browned, 5 to 7 min.
Add the rice and cook, stirring, for 1 min. Add the mushrooms and cook, stirring, for 1 min. Add the wine and cook, stirring, until almost completely reduced, about 1 min. Add 1 cup of the hot broth and cook, stirring frequently, until the broth is almost completely absorbed. Adjust the heat as needed to maintain a gentle simmer. Continue adding the broth 1 cup at a time and stirring frequently until absorbed, until the rice is tender but still toothsome (taste a few grains), 20 to 24 min. from when the first cup of broth is added. You might not need to use all of the broth. Or, if the rice still seems fairly firm when you add the last of the broth, heat and use more chicken broth as needed. Stir in the peas, Parmigiano, vinegar, and half of the mint and thyme. Season the risotto with salt and pepper to taste and serve immediately, garnished with a sprinkling of the remaining mint and thyme.