In a large pot of boiling salted water, cook pasta till tender, stirring occasionally. Drain and reserve 1/2 cup of the cooking liquid.
While pasta is cooking melt butter in heavy large skillet over medium-low heat. Add sage leaves and cook until edges curl and butter is dark amber in color (do not burn), stir and turn leaves occasionally, about 6 minutes. Remove sage from skillet and transfer sage to paper towels. Add all stock to brown butter.
Add pasta and 7 tablespoons grated Parmesan cheese to brown butter mixture in skillet; toss to coat, adding reserved cooking liquid by tablespoonfuls if dry. Season with salt and pepper. Divide among bowls. Garnish with fried sage leaves and additional cheese.