In a medium nonstick pan over medium heat, drizzle with olive oil and add sweet potatoes and garlic when oil is hot. Shake pan to combine with the oil and then add salt pepper and red pepper flakes or cayenne. Saute, shaking the pan occasionally for about 3-5 minutes so that the potatoes get a little color but not too much. 

Add stock to the pan and lay thyme sprigs on top. Cover and let simmer (reduce heat a little if you need to) about 15 minutes or until potatoes are super soft. You may need to add a little more stock if you lid doesn't fit tightly, as a lot of steam may escape and the liquid will reduce too much. I had to add about 1/2 cup more. 

When potatoes are done remove the sprigs of thyme and discard. There should be a few leaves that have fallen off and that's cool- you want that. 

Add everything to a high powered blender (like a Vitamix). Starting on low and increasing speed, blend until the liquid is totally smooth and lightens in color. You may need more stock if necessary, which you can do while you're blending in order to achieve a silky texture. Season with salt and pepper and serve with the cooked pasta right away while the sauce is still hot. (See notes)