Heat a large skillet or saucepan over medium heat. Add the oil, the garlic and the thyme and quickly cook for 30-60 seconds until garlic is fragrant, taking care not to burn.
Add in the salt, turmeric, paprika, sweet potatoes and milk, then reduce heat to low and simmer until potatoes are soft, about 15 minutes.
While the potatoes are cooking, bring a large pot of salted water to a boil. Once the water is boiling, add the noodles and cook until al dente according to the package.
Add the entire contents of the sweet potato pan to a blender along with the nutritional yeast, lemon juice and mustard. Blend until creamy and pureed.
Drain the elbow noodles, reserving 1/2 cup of pasta water, and return back to the pot. Add the sweet potato sauce and toss to combine. The sauce will likely be thick, so add the pasta water, 1-2 tablespoons at a time until desired consistency is achieved. Taste, adding more salt/pepper as needed.