Bring a large pot of water to a rolling boil, add the 1 tsp kosher salt, then drop in the elbow macaroni. Cook until al dente according to package directions (usually about 7–9 minutes). Before draining, scoop out and reserve 1/2 cup of the starchy pasta cooking water, then drain the pasta and set aside.
While the pasta cooks, whisk together the arrowroot powder and whole milk in a medium saucepan until smooth (no lumps). Heat the milk mixture gently over medium-low, stirring frequently, until it just begins to steam — do not boil.
Remove the pan from the heat and add the cottage cheese, Dijon mustard, garlic powder, smoked paprika, and black pepper. Using an immersion blender, puree the mixture in the saucepan until it becomes a smooth, velvety sauce. (If you don’t have an immersion blender, transfer to a countertop blender in batches and blend until smooth, then return to the pan.)
Return the pan to very low heat. Add the grated cheddar in two batches, whisking well after each addition until the cheese is melted and the sauce is homogenous. If the sauce seems too thick, whisk in up to 1/4–1/2 cup of the reserved pasta water a tablespoon at a time to reach your desired consistency.
Taste the sauce and adjust seasoning with salt and more black pepper as needed. Transfer the drained pasta to the saucepan and gently fold with the cheese sauce until every noodle is coated. If the mixture tightens up, stir in a splash of the reserved pasta water.
Let the mac and cheese sit off the heat for 3–5 minutes so the sauce can thicken and the flavors meld. Serve warm with an extra crack of black pepper or a light sprinkle of grated cheddar if desired.