Heat the vegetable broth in a saucepan and keep it warm over low heat.
Warm 1 tablespoon olive oil in a skillet over medium heat. Add the mushrooms and cook until browned, about 6 minutes. Season with salt and pepper, then set aside.
In the same skillet, add the remaining tablespoon of olive oil. Fry the sage leaves for 1 minute until crisp, then remove and drain on paper towels.
Melt 2 tablespoons butter in a large pot over medium heat. Add the onion and cook until soft, about 4 minutes. Stir in the garlic and cook for 1 minute more.
Add the Arborio rice and stir for 2 minutes until the edges look slightly clear. Pour in the pumpkin puree and stir until combined.
Add the warm broth one ladle at a time, stirring often. Wait until each addition is absorbed before adding the next. Continue until the rice is creamy and tender, about 18 minutes.
Remove the pot from heat. Stir in the Parmesan cheese and remaining tablespoon of butter until melted. Season with salt and pepper.
Spoon the risotto into bowls. Top with the cooked mushrooms and crispy sage leaves.