Preheat your oven to 375°F (190°C) and lightly grease a 9x13 inch baking dish with non-stick spray or butter.

Bring a large pot of salted water to a boil, add the diced potatoes and carrots, and cook for about 8 minutes until slightly tender but not fully cooked.

Add the broccoli florets to the pot with the potatoes and carrots during the last 2 minutes of boiling, then drain all the vegetables well and transfer them to a large mixing bowl.

In a separate medium bowl, whisk together the sour cream, cream of mushroom soup, minced garlic, dried thyme, salt, pepper, and 1.5 cups of the cheddar cheese.

Pour the creamy sauce mixture over the drained vegetables and toss gently until everything is evenly coated.

Transfer the vegetable mixture into the prepared baking dish, spreading it out into an even layer.

In a small bowl, combine the Panko breadcrumbs, melted butter, and the remaining 0.5 cup of cheddar cheese.

Sprinkle the breadcrumb topping evenly over the casserole.

Bake in the preheated oven for 25-30 minutes, or until the sauce is bubbly and the topping is golden brown.

Remove from the oven and let the casserole rest for 5 minutes before serving hot as a main course or side dish.