Step 1

Preheat oven to 375 F. Bring a large pot of salted water to a boil. Cook pasta until just al dente, about 9 minutes. It will finish cooking in the oven. Drain and set aside.

Step 2

In a large skillet, heat butter and olive oil. Add shiitakes and cook, untouched, for 3 minutes. Add shallots (and another 1-2 tablespoons of olive oil if your pan is dry), then stir, season with salt and pepper, and cook until shallots are soft and translucent, about 4 minutes.

Step 3

Meanwhile, shred roasted chicken breast with your hands or by using two forks and pulling the meat in opposite directions. Add chicken to mushrooms and shallots. Pour in heavy cream and sherry vinegar, then stir to combine.

Step 4

In a large bowl, combine cooked pasta, chicken and mushrooms, and 1/4 cup of asiago cheese. Mix thoroughly, then pour into a greased 2 quart (or other small) baking dish. Top pasta with remaining 2 tablespoons asiago and the grated Parmesan cheese.  Bake for 20 minutes, then top with fresh basil leaves and serve immediately.