Preheat the oven to 375°F (190°C).
Peel the potatoes and slice them into thin rounds using a mandoline or sharp knife. Place the slices in a mixing bowl with cold water to prevent browning.
In a saucepan over medium heat, melt the butter. Add the minced garlic and sauté for about 1 minute until fragrant, being careful not to burn it.
Stir in the heavy cream and milk, bringing the mixture to a simmer. Whisk in the shredded cheddar cheese, salt, black pepper, paprika, and thyme until smooth and combined. Remove from heat.
Drain and layer about half of the potato slices in the bottom of the greased baking dish. Pour half of the cheese sauce over the potatoes.
Layer the remaining potato slices on top, then pour the remaining cheese sauce over them. Sprinkle the grated Parmesan cheese on top.
Cover the baking dish with aluminum foil and bake in the preheated oven for 45 minutes.
Remove the foil and continue baking for an additional 15 minutes, or until the potatoes are tender and the top is golden brown and bubbly.
Let the dish cool for about 10 minutes before serving.