Make the cupcakes
Position a rack in the center of the oven and heat the oven to 400°F. Line a heavy-duty rimmed baking sheet with foil or parchment. Poke the sweet potatoes with a sharp knife and put them on the baking sheet. Bake until completely tender, 35 to 60 minutes, depending on the shape and moisture content of the potato; remove and set aside to cool.
Reduce the oven temperature to 350°F. Line two 12-cup cupcake tins with paper liners. When cool enough to handle, peel the sweet potatoes and purée the flesh in a food processor. Measure out 2 cups and set aside. Save the remaining potatoes for another use.
In a medium bowl, whisk the flour, baking powder, baking soda, salt, cinnamon, ginger, and cloves until well blended.
Separate the eggs. In another medium bowl, beat the egg whites with an electric hand mixer on high speed until very foamy and white, about 1 minute. With the mixer running, sprinkle in 1/4 cup of the sugar and continue to beat until very fluffy and glossy, about 3 minutes; set aside.
In a stand mixer fitted with the paddle attachment (or in a large bowl with the hand mixer), beat the butter and remaining 1-1/2 cups sugar on medium speed until very light and fluffy, scraping down the sides of the bowl as needed, 3 to 4 minutes. Beat in the egg yolks one at a time, and then add the vanilla and continue to beat 1 minute more to combine. Slowly beat in the sweet potato purée, followed by the sour cream and milk. The mixture should look smooth.
With the mixer on low, or using a rubber spatula, gently and gradually mix in the dry ingredients, mixing until each addition is just blended.
Scoop out about one-quarter of the meringue and use a spatula to fold it into the batter; gently fold in the rest of the meringue. Divide the batter between the prepared cupcake tins (about 1/4 cup for each cupcake). Once filled, lightly tap the tins on the counter to settle the batter. Bake, rotating the pans halfway through baking, until the cupcakes are puffed, lightly browned, and the center is springy when pressed lightly with a finger, 25 to 30 minutes. Be careful not to underbake the cupcakes, as they will be gummy.
Let the cupcakes sit in the pans until cool enough to handle. Carefully transfer them to a rack and let cool completely.
Make the frosting
In a stand mixer fitted with the whisk attachment (or with an electric hand mixer), whip the crème fraîche on medium speed until thick, about 1 minute (if using sour cream, skip this step). Scrape it into a medium bowl and set aside.
Switch to the paddle attachment if using a stand mixer, and put the butter in the mixing bowl. Beat until light and fluffy, about 2 minutes. With the mixer running, add the cream cheese, one chunk at a time, and beat until smooth, about 2 minutes. Slowly beat in the syrup, vanilla, and 1/4 tsp. salt until incorporated. Gradually sprinkle in the confectioners’ sugar and beat until very smooth, about 3 minutes.
Fold one-quarter of the cream cheese mixture into the crème fraîche. Then fold the mixture back into the cream cheese frosting just until thoroughly blended.
Fill and frost the cupcakes Using a 1/4-inch plain pastry tip (Ateco #801), punch a hole into the top of each cupcake, pushing the tip in at least 1/2 inch
Fit the tip onto a pastry bag and fill the bag with 1-1/2 cups of frosting. Insert the tip into the hole in the top of one of the cupcakes and squeeze the bag lightly to fill with about 1 Tbs. filling. As you fill the cupcake, pull the bag upwards. Don’t worry if some of the frosting comes out of the hole. Repeat with the remaining cupcakes.
Dollop 2 Tbs. of the remaining frosting on top of each cupcake. Using a small offset spatula or butter knife, spread the frosting over the tops. Lightly sprinkle with ground cinnamon (if using) and serve.