Heat oven to 375°F. Grease a 9x13-inch baking dish.
Boil spaghetti in salted water until just shy of al dente. Drain and set aside.
Warm olive oil and 2 tbsp butter in a large skillet over medium-high heat.
Brown mushrooms until they release liquid and develop color, about 6 minutes.
Stir in onion; cook until soft, 3 to 4 minutes. Add garlic; cook 30 seconds.
Melt remaining butter. Sprinkle in flour and cook, stirring, for 1 minute.
Deglaze with wine, scraping the pan. Whisk until smooth and slightly thick.
Slowly whisk in broth, then half-and-half. Simmer until creamy and thickened.
Blend in cream cheese until melted. Stir in 1 cup Parmesan, salt, pepper, and Italian seasoning.
Fold in chicken, peas, and parsley. Add cooked spaghetti and toss to coat.
Spread mixture in the baking dish. Mix panko with melted butter and remaining Parmesan; sprinkle over top.
Bake until bubbling and golden, 20 to 25 minutes. Rest 10 minutes before serving.