NOTE: Dough will be slightly softer than most. Handle as briefly and as gently as possible when shaping. Overworking the dough results in flatter cookies.
Adjust oven rack to middle position and heat oven to 350 degrees. Line 2 large rimmed baking sheets with parchment paper.
Whisk flour, baking soda, baking powder, and salt together in medium bowl. Set aside.
Place 1 1/2 cups sugar and cream cheese in large bowl. Place remaining 1/3 cups of sugar in shallow baking dish or pie plate and set aside. Pour warm butter over sugar and cream cheese and whisk to combine (some small lumps of cream cheese will remain but will smooth out later). Whisk in oil until incorporated. Add egg, milk, and vanilla; continue to whisk until smooth. Add flour mixture and mix with rubber spatula until soft homogenous dough forms.
Divide dough into 24 equal pieces, about 2 tablespoons each (can use #40 portion scoop). Using hands, roll dough into balls. Working in batches, roll balls in reserved sugar to coat and evenly space on prepared baking sheet, 12 dough balls per sheet. Using bottom of a drinking glass, flatten dough balls until 2" in diameter. Sprinkle tops evenly with 4 teaspoons of sugar remaining in shallow dish (2 teaspoons per baking sheet), discarding any remaining sugar.
Bake, one sheet at a time, until edges are set and just beginnning to brown, 11 to 13 minutes, rotating sheet after 7 minutes. Cool cookies on baking sheet 5 minutes. Using wide spatula, transfer cookies to wire rack and cool to room temperature.