Preheat oven to 350 degrees F.
Remove chicken from bones and shred. Bones and skin can be tossed inyour Instant Pot with water for a couple hours to make some chicken broth for later! Combine shredded chicken with ham, swiss cheese, and chicken broth in large casserole dish.
In a separate bowl, combine bread crumbs, parmesan, melted butter and garlic herb seasonings. Sprinkle over chicken. Cover and bake until heated through and cheese has melted, about 20 minutes.
While the casserole is cooking, make the sauce. In a saucepan melt the butter, then add the flour and whisk together. Cook for several minutes while continually whisking to avoid burning.
Gradually whisk in milk. Continue to heat until the milk bubbles and begins to thicken, about 3-5 minutes. Remove from heat and whisk in dijon, parmesan, and thyme. Add salt and pepper to taste.
To serve, pour warm sauce over casserole.