In a large pot of salted boiling water, cook pasta according to package directions until al dente.
Drain, reserving 1/2 cup pasta water, and return to pot.
In a large skillet over medium-high heat, heat olive oil.
Season chicken with salt and pepper.
Sear chicken until golden and no longer pink, about 8 minutes per side.
Transfer to a plate to let rest, then cut into 1-inch cubes.
Meanwhile, return skillet to medium-high heat and melt butter.
Cook mushrooms until golden, about 5 minutes, then add garlic and onions and cook, stirring occasionally, 4 to 5 minutes.
Add flour and stir until incorporated.
Add half-and-half, chicken stock, Parmesan, and oregano, and season with salt and pepper.
Bring to a boil, then reduce heat and simmer, 5 minutes.
Fold cooked pasta into sauce with chicken (and its juices) and arugula.
If sauce is too thick, add pasta water until you reach desired consistency.
Top with more Parmesan and serve.
Enjoy your creamy chicken and mushroom pasta!
