Preheat oven to 375F. Line a sheet pan with parchment paper.

Fill a large stock pot with water, add 3 tablespoons of salt and bring to a boil. Turn down to simmer and cover until ready to cook the pasta. 

Rub every crevice of the chicken breast generously with olive oil, then sprinkle with salt and black pepper. 

Place on the sheet pan and bake for about 35 minutes. Remove from the oven and brush the top of the chicken with the pan juices. Return to oven for 5 minutes to brown the top. (If more browning is needed, baste again, increase the oven temperature, and bake for another 5 minutes.) Remove the chicken from the oven and let cool. Using your hands, tear the chicken breast into chunks and set aside. See Teri tip below.

In a large skillet over medium heat add 2 tablespoons butter and 3 tablespoons extra virgin olive oil, stirring until the butter is melted and combined with the oil. Add the mushrooms and cook until golden brown, for 7 to 9 minutes. Remove and set aside in a large bowl.

In the same pan over medium heat, add 1 tablespoon butter and 2 tablespoons olive oil, stirring until melted and combined. Add the broccolini, a pinch of salt and cook until crispy and lightly browned, for 2 -3 minutes.  Remove from heat and transfer to the bowl with the mushrooms.  

Bring the hot pasta water back to a full boil, add the pasta and cook according to the package instructions. 

In the same sauté pan, over medium heat add 1 tablespoon olive oil and the garlic, and cook for about 30 seconds. Add the wine and cook about 30 seconds. Add 2 tablespoons of butter and 3 tablespoons of olive oil,  stirring to combine and melt the butter. Add the chicken, vegetables, and all the juices in the bowl,  stirring to combine. Add ½ cup heavy cream and stir to combine and bring to heat, about 1 minute. Add 1 cup parmesan and stir until combined.

Warm a large serving bowl. Add some sauce to the bottom of the bowl.  Then add the cooked pasta to the bowl and top with the remaining sauce. Add black pepper and toss. Top with chopped parsley. I like to add the remaining 1 cup parmesan and toss it all together. Or, keep it a little lighter and omit this final cup of parmesan. If the sauce becomes too thick, add pasta water 1/4 cup at a time and toss. Serve.