Pasta Carbonara with Cabbage and Mushrooms

Ingredients

• 1 tablespoon extra-virgin olive oil
• 8 ounces shiitake mushrooms, stems removed, sliced into 1/2-inch strips
• 6 ounces bacon, sliced crosswise into 1/2-inch strips
• 8 ounces tagliatelle or linguine
• 3/4 tsp. kosher salt, plus more
• 1 medium head of savoy cabbage (about 1 pound) cored, sliced into 1/4-inch ribbons
• 2 large egg yolks
• 2 ounces Parmesan, finely grated, divided, plus more for serving
• 1 1/2 teaspoons freshly ground black pepper

Directions

1. Heat oil in a large heavy skillet, preferably cast iron, over high. Cook mushrooms and bacon, stirring often, until browned and crisp, about 8 minutes. Using a slotted spoon, transfer to a paper towel-lined plate; set aside. Reserve fat in skillet.
2. Meanwhile, cook pasta in large pot of boiling salted water, stirring occasionally, until al dente. Drain, reserving 1 1/2 cups pasta cooking liquid.
3. Heat skillet with reserved fat over high. Add cabbage, press into an even layer, and cook, undisturbed, 2 minutes; season with remaining 3/4 tsp. salt. Turn cabbage with tongs, then continue to cook, undisturbed, until lightly charred in places and still crisp in others, about 2 minutes more.
4. Whisk egg yolks, 1 oz. Parmesan, and 3/4 cup pasta cooking liquid in a large bowl until a smooth, glossy sauce forms. Add pasta and stir to coat. Add reserved mushrooms and bacon, cabbage, pepper, and 1 oz. Parmesan and toss again, adding more pasta cooking liquid if needed to loosen sauce.
5. Divide pasta among bowls. Top with more Parmesan.