Preheat oven to 375°F, grease 9x13-inch baking dish with butter
Peel potatoes, slice into ⅛-inch rounds with mandoline or knife
Place in cold water to prevent browning
Melt 4 tbsp butter in saucepan over medium heat
Add garlic, cook 1 minute until fragrant
Whisk in flour, cook 2-3 minutes until golden and bubbling
Gradually whisk in warm milk, ½ cup at a time
Whisk in cream, bring to gentle simmer
Cook 3-5 minutes until thickened
Stir in salt, pepper, thyme, nutmeg, paprika
Drain potatoes, pat dry
Layer ⅓ potatoes in baking dish, season lightly
Pour ⅓ sauce over, sprinkle with ⅓ cheddar
Repeat with another ⅓ potatoes, ⅓ sauce, ⅓ cheddar
Top with remaining potatoes, pour remaining sauce
Cover tightly with foil
Bake 45 minutes covered
Remove foil, sprinkle remaining cheddar and all Parmesan
Bake uncovered 25-30 minutes until fork-tender and golden
Rest 10-15 minutes before serving
Garnish with parsley and thyme
Serve hot