Mix together the white cheddar, Jarlsberg, and parmesan cheeses until well combined. Set aside 1 cup of the cheese mixture for the topping.
Preheat broiler to low with the oven rack near the top of the oven.
In a large skillet, over medium-high heat, bring the heavy cream to a boil.
Reduce heat to low. Add garlic and gently simmer, stirring often (about 2 minutes).
Stir in cooked pasta and return to a simmer over medium heat. Cook and stir for about a minute. Remove from heat.
Add the cheese mixture and stir until the cheese has melted.
Gently stir in the crab and 1 tablespoon of chives. Season with salt, if needed.
Top with the 1 cup of cheese mixture you had set aside. Broil for 5-7 minutes, or until the cheese is golden brown.
Let it sit for 5-10 minutes, and add the remaining chives for garnish.