01 - Bring a large pot of salted water to a rolling boil. Cook the pasta until al dente, following package directions. Reserve ½ cup of the pasta cooking water before draining the pasta thoroughly.
02 - While the pasta is cooking, prepare the sage glass shards. Pat the sage leaves completely dry. In a small bowl, whisk the egg white until it becomes frothy and lightly aerated. Dip each sage leaf into the frothy egg white, ensuring it's coated on both sides. Immediately dust both sides of the coated leaf with cornstarch. Heat approximately 1 cm (½ inch) of neutral oil in a small skillet over medium-high heat. Carefully fry the coated sage leaves for about 20-30 seconds, or until they appear crisp and translucent. Remove the crisped sage leaves with a slotted spoon and drain them on paper towels. Set aside for later garnishing.
03 - In a large skillet, melt the unsalted butter over medium heat. Add the remaining 16-20 fresh sage leaves to the melting butter. Continue to cook, swirling the pan frequently, until the butter begins to foam and develops a rich golden-brown hue, which should take about 3-4 minutes. Once the sage leaves are crisp, remove them from the pan with a slotted spoon and reserve them for garnish.
04 - Add the finely minced garlic to the browned butter in the skillet. Sauté for approximately 30 seconds until the garlic becomes fragrant. Carefully remove the skillet from the heat. Stir in the fresh lemon juice to balance the richness of the butter.
05 - Add the drained, cooked pasta directly into the skillet with the brown butter sauce. Toss the pasta gently to ensure it is thoroughly coated. If necessary, add small amounts of the reserved pasta water to achieve a silky and cohesive sauce consistency. Incorporate the freshly grated Parmigiano-Reggiano cheese and toss again until melted and integrated. Season generously with freshly ground black pepper to taste.
06 - Plate the finished pasta attractively. Garnish the dish with the reserved crispy brown butter sage leaves. Artfully arrange the delicate sage glass shards on top of the pasta to create a dramatic visual presentation. Serve immediately while hot.