Preheat oven to 375°F and grease a 9x13 baking dish.
Peel and slice potatoes into even rounds; arrange in the bottom of the dish.
Sauté chicken pieces with mushrooms and red pepper until just cooked; season with thyme, salt, and pepper.
Melt butter, cook garlic briefly, then whisk in cream and milk; simmer until slightly thickened.
Stir chicken mixture and peas into the sauce.
Spoon the filling evenly over the potato layer.
Top with shredded mozzarella.
Bake 30–35 minutes until golden and bubbly.
Rest 5 minutes, garnish with parsley, and serve.
Tip: Let the casserole rest so clean slices hold together.