Gather all ingredients. Preheat the oven to 400 degrees F (200 degrees C). Grease a 3-quart rectangular baking dish.
Bring a 4 to 6-quart Dutch oven filled with salted water to a boil, and cook pasta until tender with a bite, 9 to 11 minutes, adding peas and asparagus for the last 3 minutes of cooking time. Drain, reserving 2/3 cup of the pasta water. Hold pasta in the strainer; set Dutch oven aside to use for making the sauce.
Meanwhile, heat oil in a 12-inch skillet over medium-high heat. Season chicken with 1/2 teaspoon salt and 1/2 teaspoon black pepper. Add chicken to hot oil. Cook, stirring occasionally, until chicken is golden and fully cooked, 5 to 7 minutes. An instant-read thermometer inserted near the center should read at least 165 degrees F (74 degrees C). Remove from heat.
For sauce, melt butter in the Dutch oven. Whisk in flour, remaining 1/2 teaspoon salt and 1/4 teaspoon pepper. Whisk in milk, cream cheese, and chicken broth. Cook and stir over medium heat until thickened and bubbly. Cook and stir 1 minute more. Whisk in reserved pasta water, 2/3 cup Parmesan cheese, basil, and oregano.
Add pasta mixture to the Dutch oven with sauce; toss to coat. Stir in cooked chicken, spinach, and cherry tomatoes.
Spoon mixture into prepared baking dish. Sprinkle with remaining 1/3 cup Parmesan cheese and panko bread crumbs.
Bake in the preheated oven until sauce is bubbly and topping is golden brown, 15 to 20 minutes.
