Pasta Carbonara with Cabbage and Mushrooms

Name: 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