Preheat the oven to 375 degrees F. Melt 1 tablespoon butter in a large ovenproof skillet over medium-high heat. Add the onion, potatoes and frozen peas and carrots and cook, stirring occasionally, until the vegetables begin to soften, about 5 minutes. Add the ham, flour and thyme and cook, stirring, until combined. Stir in the chicken broth and bring to a boil, then stir in the milk and simmer until slightly thickened, about 3 minutes. Transfer the skillet to the oven and bake until the potatoes are tender, about 20 minutes.
Meanwhile, melt the remaining 3 tablespoons butter in a medium skillet over medium-high heat. Add the panko, parsley and 1/8 teaspoon each salt and pepper and cook, stirring occasionally, until the panko is slightly toasted, about 4 minutes. Scatter over the ham and vegetable mixture; let rest 5 minutes before serving.