One-Pot White Wine Pasta with Mushrooms and Leeks

Ingredients

3 tablespoons extra-virgin olive oil
1 pound cremini mushrooms, trimmed and sliced
2 tablespoons unsalted butter
2 medium leeks, trimmed and thinly sliced (white and light green parts only), about 1 1 /2 cups
4 medium garlic cloves, thinly sliced
2 1/2 teaspoons kosher salt, divided
1 pound short pasta, such as penne, casarecce, or pipe rigate
3 cups water
1 1/3 cups low-sodium vegetable broth
2/3 cup dry white wine
1/2 cup heavy whipping cream
1/2 cup grated Parmigiano-Reggiano cheese (about 2 ounces), plus more for serving
2 tablespoons chopped fresh dill
2 tablespoons chopped fresh flat-leaf parsley
1 teaspoon grated lemon zest plus 1 1/2 teaspoons fresh juice (from 1 lemon)
1/2 teaspoon black pepper