Pour the vegetable broth into a large saucepan and bring to a boil over high heat. When boiling, lower the heat to low, cover the saucepan, and keep the liquid hot. In case additional liquid is required, fill an additional small saucepan with water and place on the stove over a high heat until boiling. Once boiling, lower heat, cover and keep hot.
In a heavy-bottom saucepan, heat olive oil and 1 tablespoon butter over medium-high heat until butter foams. When foaming subsides, add the mushrooms and cook, stirring occasionally, until browned and any liquid they release is evaporated, about 4 minutes. Add sage, season with salt and pepper and transfer to a bowl using a slotted spoon. Set aside.
Return the saucepan to medium heat. Add 2 tablespoons butter and heat until butter foams. When foaming subsides, cook shallots until softened, stirring frequently with a wooden spoon, about 3 to 4 minutes. Add rice and stir until begins to turn opaque, about 2 minutes. Add the wine and, using a wooden spoon, scrape any browned bits from the bottom of the pan.
Once the liquid has been absorbed, increase heat to medium and, using a ladle, add about 1 cup of hot broth to the rice. Cook, stirring constantly with a wooden spoon over medium heat until broth is almost fully absorbed. Add the remaining stock ½ cup at a time, stirring constantly and adding more broth only after the previous addition has been absorbed, until the rice begins to pull away from the sides of the pan, about 16 to 20 minutes.