Bring a large pot of salted water to a boil. Add the short pasta and cook according to package instructions, making sure it's slightly al dente. Drain the pasta and set it aside without rinsing, allowing a little starch to help the sauce cling later.
Place a steamer basket in a large saucepan and pour in 1½ cups water. Add the finely chopped cauliflower and diced sweet potatoes to the basket. Cover, bring water to a boil, then reduce to a simmer and steam for 8-10 minutes, until the vegetables are fork tender.
Transfer the steamed cauliflower and sweet potatoes from Step 2 to a blender. Add 1/2 cup of the full fat milk and blend until the mixture is completely smooth.
In a large pot over medium heat, melt the ghee and whisk in the arrowroot starch until you form a smooth roux. Slowly add the remaining 3/4 cup full fat milk, whisking constantly. Continue whisking until the mixture just starts to boil and thickens slightly.
Reduce the heat to the lowest setting. Add the shredded extra sharp cheddar cheese, blended veggie purée from Step 3, garlic powder, dijon mustard, sea salt, and ground black pepper. Stir continuously until the cheese fully melts and the sauce is silky. I like to taste the sauce at this point and add a tiny extra pinch of salt if needed for maximum flavor.
Remove the cheese sauce from the heat. Add the cooked pasta from Step 1 and gently stir until all the pasta is coated in the sauce. Serve immediately, or for a crispy top, transfer to a baking dish and broil for about 5 minutes until golden and bubbly.