Using an electric mixer, cream together cream cheese and butter in a large bowl until creamy and smooth. Beat in sugar, lemon zest, lemon juice, vanilla, lemon oil, and salt. Mix until well combined; the mixture should be light and fluffy.
Add egg and egg yolk and beat in well for about two minutes at medium speed.
At low speed, gradually add flour and baking powder and mix until just incorporated.
The dough will be very sticky. Cover the bowl with saran wrap and refrigerate it overnight.
The next day, preheat the oven to 350 degrees. Line a baking sheet with parchment paper; set aside. Place powdered sugar in a small bowl and set aside.
Using a spring-loaded cookie scoop, measure out the cookie dough and place them on the baking sheet at least 2 inches apart. On a standard size cookie sheet, I am typically able to fit 12 cookies.
One by one, toss each cookie dough ball in the powdered sugar and shake around until each has been thoroughly coated. Return the baking sheet and repeat with all of the dough.
Bake until cookies have spread into round cookie shapes and are puffed and crackly, about 15 minutes. Do not overbake. The cookies will still be soft in the centers. If they start to brown around the edges, they have baked too long. The underside of the cookies should be lightly browned.
Remove from the oven and allow the cookies to cool on the sheet for a couple of minutes. Transfer to wire rack and allow cookies to cool completely. Serve immediately or store in an airtight container for up to a week.