In a medium pot, bring the stock, salt and pepper to a simmer over medium-high heat. Reduce the heat to low and cover to keep warm.
In a large pot, heat the oil and melt the butter until foamy over medium-high heat. Add the shallots, garlic and duck liver, if using, and cook, stirring, for 1 minute. Add the mushrooms, and cook, stirring, until the mushrooms give off their liquid, about 3 minutes. Add the rice, stirring to coat with oil and cook, stirring constantly, until opaque, about 2 minutes. Add the wine to deglaze the pan and cook, stirring, until the liquid is reduced by half, about 1 minute. Reduce the heat to medium. Add 1 cup of the hot stock, and cook, stirring constantly until nearly all the liquid has been absorbed. Continue adding more stock 1/2 cup at a time as it is absorbed, and cook, stirring constantly, until the rice is tender and just al dente, about 12 minutes total cooking time. When all the stock has been added, fold in the duck meat, reserved pumpkin butter, thyme and oregano. Add 1/2 cup of the cheese and mix well. Remove from the heat.
Place the pumpkins in the center of 4 large serving plates and surround each with a sprinkling of pumpkin seeds. Divide the risotto among the pumpkins and top each serving with 2 tablespoons of the remaining Parmesan. Place the lids on the pumpkins and serve immediately.