Combine the cream cheese, sugar, and vanilla (by hand or with a mixer) in a small bowl. Use a spoon to make 15 small, teaspoon-sized balls, and arrange them on a plate. Chill the plate in the freezer so that they firm up.
Spread the canned pumpkin out on a plate, press it with paper towels to soak up moisture, and repeat a few times until it dries out.)
Using an electric hand mixer cream the butter with the sugars until light and fluffy. Beat in the egg yolk, vanilla, and pumpkin puree. Add the pumpkin pie spice, baking soda, salt, and cream of tartar, and beat until combined, scraping the bottom and sides of the bowl as needed. Add the flour and mix just until a soft dough forms. Wrap the dough in plastic and chill the dough for at least 20 minutes, or up to overnight.
Preheat the oven to 375ºF, arranging racks in the top and bottom thirds of the oven. Line two baking sheets with parchment paper.
Make the spiced sugar by mixing together the sugar and pumpkin pie spice in a small bowl.
Portion the dough into 15 balls. To add the filling, split each portion in half and flatten each piece with the palm of your hand. Place the chilled cream cheese ball into the center of one piece, then sandwich the other piece on top. Roll it into a ball so that the cream cheese is sealed inside. Then roll it through the sugar, and arrange on the prepared baking sheet. Repeat with the rest of the dough and cream cheese filling, putting 7 or 8 cookies on each baking sheet.
Bake for 11 to 14 minutes, until the cookies begin to brown along the edges and are puffed in the centers. Cool completely on the pans before eating.