Preheat your oven to 190°C (375°F) and lightly grease a medium baking dish.
Using a sharp knife or mandoline, thinly slice the zucchini, carrots, and potatoes into about 3mm thick rounds. Keep the slices uniform for even cooking.
Layer the vegetables in the prepared dish, starting with a layer of potatoes, then zucchini, then carrots. Season each layer with salt, pepper, and a sprinkle of thyme. Repeat until the dish is filled, ending with a layer of cheese on top.
In a small saucepan, warm the heavy cream over medium heat until it just begins to simmer. Stir in most of the grated cheese until melted and smooth, then pour evenly over the layered vegetables.
In a small skillet, toast the panko breadcrumbs with olive oil until golden and crispy, about 2-3 minutes. Sprinkle the toasted breadcrumbs evenly over the top of the dish for added crunch.
Bake the gratin uncovered for 40-45 minutes, until the top is golden brown and bubbling around the edges. Check that the vegetables are tender when pierced with a fork.
Remove the gratin from the oven and let it rest for 10 minutes. This helps the layers set and makes slicing easier.
Slice into portions and serve warm, enjoying the crispy top and tender, cheesy vegetables inside.