Preheat the oven to 375 degrees F. Line a rimmed baking sheet with aluminum foil or parchment paper.
Scrub the sweet potatoes, then pierce all over with the tines of a fork. Place the potatoes on the prepared baking sheet. Bake until fork-tender, about 50 minutes to 1 hour 15 minutes, depending upon the size of your potatoes. Remove the sweet potatoes from the oven and let cool slightly.
While the potatoes bake, cut the cream cheese and butter into a small dice. Let come to room temperature while the potatoes bake (you can also melt the butter if you prefer).
Once they are cool enough to handle, carefully cut off the top third of the 4 largest sweet potatoes lengthwise so that you have an open sweet potato boat (reserve the 5th, smallest sweet potato). With a spoon, scoop out the potato flesh from the base and transfer it to a food processor fitted with a steel blade. Leave a thin inner layer of sweet potato flesh lining the inside of the base so that it holds its shape. Scrape the flesh away from the cut tops and discard the peels or save for compost. Return the bases to the same baking sheet.
Split the final, smallest sweet potato in half and scoop all of the flesh into the food processor. Discard the peel or use it for compost (the extra sweet potato flesh will allow you to impressively fill up the bases).
To the food processor, add the Greek yogurt, salt, cinnamon, nutmeg, black pepper, cayenne pepper, cream cheese, and butter. Process until the ingredients are very well blended and the puree is ultra smooth and light, stopping to scrape down the bowl as needed. Taste and adjust the seasoning as desired. (I add a pinch more salt; if you'd like more of a kick, add a bit more cayenne.)
Generously mound the sweet potato bases with the filling, piling it high (we are going for presentation here!), then sprinkle the pecans evenly over the top.
Return the sweet potatoes to the oven and bake for 10 minutes, until the pecans are crisp and the filling is heated through. Enjoy warm.
TO MAKE AHEAD: Up to 1 day in advance, scrub, pierce, and bake the sweet potatoes as directed. Refrigerate them in an airtight storage container until you're ready to finish the recipe.
TO STORE: Refrigerate sweet potatoes in an airtight storage container for up to 4 days.
TO REHEAT: Rewarm leftovers in a baking dish in the oven at 350 degrees F or in the microwave.