Position racks in the middle and upper third of the oven; preheat to 400 degrees F. Scrub the potatoes and dry well. Bake directly on the middle oven rack until easily pierced with a knife, 45 to 50 minutes. Remove from the oven; let cool 5 minutes.
Meanwhile, heat 3 tablespoons olive oil in a large skillet over medium-high heat. Add the mushrooms; cook, stirring occasionally, until browned, about 5 minutes. Season with 1/4 teaspoon salt. Reduce the heat to medium; add the onion and cook, stirring occasionally, until translucent, about 4 minutes. Add the sage and chicken broth. Reduce the heat to medium low and simmer until the vegetables are tender, about 3 minutes. Increase the heat to medium high and cook until most of the liquid evaporates, about 2 more minutes; set aside.
One at a time, hold each potato with a kitchen towel and halve lengthwise. Scoop the flesh into a large bowl, leaving a 1/4-inch-thick shell. Mash the flesh with the butter, taleggio and parsley until just combined. Stir in the mascarpone, then the mushroom mixture. Brush the potato skins with the remaining 1 tablespoon olive oil and season the insides with salt and pepper. Set on a baking sheet.
Mound the filling into the potato skins and sprinkle with the parmesan. Return to the oven on the top rack; bake until the filling starts browning and the skins are crisp, 18 to 20 minutes. Season with salt.