Combine the chicken broth and 3 cups water in a medium saucepan and bring to a gentle simmer. Put the porcini mushrooms in a spouted measuring cup and ladle 1 cup hot stock over. Let soak 15 minutes. Remove the mushrooms, reserving the soaking liquid, and finely chop. Pour the soaking liquid back into the broth.
Heat 1 tablespoon olive oil in a large skillet over medium heat, then add the butternut squash and season with salt and pepper. Cook, tossing occasionally, until lightly browned and almost tender, about 10 minutes. Remove to a plate.
Add the remaining 2 tablespoons olive oil to the skillet and turn to medium-high heat. Scatter in the fresh mushrooms and cook, stirring occasionally, until the mushrooms are well browned and have given up their liquid and the liquid has reduced away, 7 to 8 minutes. Reduce the heat to medium and add the shallots. Cook, stirring occasionally, until wilted, about 3 minutes. Add the rice and stir to coat in the olive oil. Let the rice toast in the skillet for a minute, then stir in the reserved chopped porcini.
Add the white wine. Bring to a simmer and cook until absorbed. Ladle in enough of the hot stock to just cover the rice. Adjust the heat so the risotto is gently simmering. Cook and stir the rice until the liquid is almost absorbed, then ladle in more stock just to cover. Continue to stir and add stock until the rice is al dente, adding the squash in the last 6 minutes of cooking time, 18 to 20 minutes. You may have a little bit of stock left over, and that's OK.)
Remove the risotto from the heat and stir in the butter, cheese and parsley. Serve immediately, passing additional Parmesan at the table.