Cook the pasta. Set a large pot of water over high heat. Add enough salt to make the water taste like the ocean (that's usually about 1/4 cup). When the water comes to a boil, pour in the pasta. Stir it continuously for the first minute. Cook the pasta according to the directions on the package. Each gluten-free pasta cooks differently. You are looking to cook the pasta until it has softened but still has a good bite. That's usually around 8 to 10 minutes.
Set up the sauce. Spread the Cheddar over the bottom of a large bowl. Dot the top of the Cheddar with the goat cheese. Toss in the kale leaves.
Finish the dish. When the pasta is cooked al dente, use a slotted spoon to transfer it to the bowl, on top of the cheeses and kale. Transfer about 1/2 cup of the pasta cooking water as well to the bowl. Do not stir. Let it sit for 5 minutes.
After 5 minutes, stir up the cheeses and pasta. You should have a good, creamy sauce. If it's not quite creamy enough yet, add a few more tablespoons of pasta water. Serve immediately.