Pre-heat oven to 350° F.
Spray a bundt pan with baking spray and dust with flour. Set aside.
In a large bowl, beat butter and cream cheese at medium speed with a mixer until fluffy, 3 to 4 minutes.
Mix in the sugar and brown sugar until incorporated, about another 3 minutes.
Add eggs, one at a time, beating well after each addition.
Add sweet potato and vanilla, beating until combined.
In a medium bowl, whisk together flour and 1 1/2 teaspoons pumpkin pie spice.
Gradually add flour mixture to sweet potato mixture, beating at low speed just until combined.
In a small bowl, stir together the remaining 1/3 cup sugar, remaining 1 tablespoon brown sugar, and remaining 1 tablespoon pumpkin pie spice.
Spoon 1/3 of the batter into prepared pan (batter will be thick and a little sticky), spreading evenly.
Sprinkle half of the sugar-spice mixture over batter.
Repeat the process once and then top with remaining batter.
Tap pan a few times to release air bubbles.
Bake until an inserted wooden toothpick near center comes out clean, approximately 50 minutes.
Let cool in the pan for 10 minutes.
Carefully remove the cake from pan and let cool completely on a wire rack.