Preheat oven to 375˚F. Grease a 9”x13” baking dish with 2 tablespoon butter.
Place a large skillet over medium-high heat, add oil and melt 1 1/2 tablespoons butter.
Add onion and sauté for 5 to 6 minutes.
Add mushrooms and garlic and continue to sauté for an additional 3 to 4 minutes. Season with salt and pepper.
Add herbs and shredded chicken to the mushroom mixture, toss together and continue to sauté for 1 minute. Set aside.
In a saucepan, melt 3 ½ tablespoons butter over medium heat.
Add flour and whisk together until no lumps remain and the raw flour taste has been cooked out, 2 to 3 minutes.
Pour milk into the mixture and whisk until smooth. Continue to whisk until the mixture is thick enough to coat the back of a wooden spoon. Season with salt and pepper.
Stir ½ cup Parmesan into the béchamel and allow mixture to simmer for 1 minute.
Add stock and continue to simmer for 1 minute.
Add chicken mixture, pasta, reserved pasta water, and peas to sauce and toss together until fully combined. Sprinkle ¼ cup Parmesan over the mixture and toss together. Adjust seasonings if needed.
Pour pasta mixture into the prepared baking dish and set aside.
In a small skillet, melt the remaining 1 tablespoon butter and toss together with panko. Season with salt and pepper.
Sprinkle evenly over the pasta mixture and top with remaining Parmesan.
Bake tetrazzini in the oven for 20 to 25 minutes or until the panko has browned and the entire dish is bubbling. Cool for 10 minutes before serving.