Adjust oven rack to upper-middle position and heat oven to 425 degrees
In a medium bowl, combine the cheeses together; set aside
Bring potatoes, cream, broth, thyme, salt, pepper, nutmeg, paprika, and crushed chiles to a simmer in a large saucepan over medium-high heat
Reduce heat to medium, cover, and cook, stirring occasionally, until a paring knife can be slipped in and out of the potatoes with no resistance, about 8 minutes, adjusting heat as necesary to maintain a gentle simmer
Off heat, remove the thyme sprigs, and gently stir in 1 cup of the cheese mixture
Transfer the potato mixture to a 13 b 9-inch baking dish, spread into an even layer, and sprinkle with the remaining 1 cup of cheese mixture
Bake until bubbling around the edges and the top is golden brown, about 20 minutes
Let cool for 15 minutes before serving