1. Bring 4 quarts of salted water to a boil. Add pasta and cook, stirring often, until just starting to soften (about 5 minutes). Drain pasta and toss with 1 tbsp or oil; leave in colander and set aside.

2. Dry now-empty pot and heat remaining 1 tablespoon oil over medium heat until shimmering. Add mixed mushrooms, onion, porcini mushrooms, and salt. Cover and cook to soften until mushrooms have released their liquid (about 10 minutes). Uncover, increase heat to medium-high, and continue to cook until mushrooms are dry and browned, 5 to 10 minutes

3. Stir in garlic and thyme and cook until fragrant (about 30 seconds). Add flour and cook, stirring constantly, until golden, about 1 minute. Slowly whisk in broth and wine and bring to a simmer.

4. Adjust oven rack to middle position and heat oven to 400ºF.

5. Season chicken with salt and pepper and nestle into pot. Reduce heat to low, cover, and simmer gently until chicken registers 160 degrees, about 15 minutes. Transfer chicken to cutting board let cool slightly, then shred into bite-size pieces using 2 forks. 

6. Remove the pot from heat and gradually whisk cream, 1 cup Gruyere, ½ cup Parmesan, and vinegar into sauce until cheese is melted and sauce is smooth. Stir in shredded chicken and pasta, breaking up any clumps. Season with salt and pepper to taste. Transfer mixture to 9×13 baking dish and sprinkle with remaining Gruyere and Parmesan.

7. Place baking dish on aluminum foil-lined rimmed baking sheet and bake until golden and bubbling around edges, 25 to 35 minutes. Let casserole cool 20 minutes. Sprinkle with chives and serve.