Begin by preheating your oven to 375 degrees. Line a muffin tin with paper muffin liners and set aside.
Sift together the flour, pumpkin spice, baking soda and salt. Set aside.
In large bowl, use a handheld mixer to beat together the pumpkin puree, sugar, and brown sugar. Beat in the eggs, vegetable oil, and vanilla.
Next, on low speed, blend in the flour mixture.
Fill the paper muffin liners about ¾ way full and set aside.
In a clean bowl, and with clean attachments on your handheld mixer, beat cream cheese until smooth. Add in the sugar, egg yolk, and vanilla; mix until incorporated.
Use a tablespoon to scoop the cream cheese mixture onto the top of each muffin. Just spoon it over top – about one tablespoon for each muffin will do just fine. Use a toothpick to drag the cream cheese mixture through the pumpkin mixture. Be sure to drag the toothpick from side to side without spilling the batter over the side. Also, be careful to not touch the bottom of the paper liner, but go deep enough so that both batters are being slightly blended.
Place the muffins in the oven on the middle rack and bake for 18 minutes. Allow to cool for two minutes in the muffin pan before transferring to a wire cooling rack to finish the cooling process.