Preheat oven to 375°F (190°C). Grease a 9×13 inch baking dish with olive oil.
Peel the potatoes and slice thinly (about 1/8 inch) using a knife or mandoline.
Heat olive oil in a saucepan over medium heat. Cook the diced onion and garlic for 3 minutes.
Whisk the cornstarch into the coconut milk until smooth. Add to the saucepan along with the vegetable broth, thyme, salt, and pepper. Simmer for 3–4 minutes until slightly thickened.
Layer half the potatoes in the baking dish. Pour half the sauce over them. Repeat with remaining potatoes and sauce.
Cover tightly with foil and bake for 45 minutes. Remove foil and bake 20 minutes more until the top is golden and potatoes are tender.
Let rest 10 minutes before serving.
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