Combine sugar and lemon zest in a food processor and pulse several times to bruise lemon zest. Transfer 1/2 cup sugar mixture to a bowl.
Beat butter and cream cheese in a mixing bowl until creamy and well-combined; mix in remaining lemon-sugar mixture, egg, lemon juice, and vanilla extract. Use an electric mixer to beat baking powder and salt into moist ingredients; gradually beat flour into mixture to make a dough. Freeze dough for 1 hour.
Preheat oven to 350 degrees F (175 degrees C). Grease a baking sheet.
Shape dough into 1-inch balls and roll in reserved 1/2 cup lemon sugar. Place 2 inches apart on prepared baking sheet. Press cookies down slightly to flatten and sprinkle each cookie with about 1/8 teaspoon of the remaining lemon sugar.
Bake in the preheated oven until cookies are firm on bottoms, 10 to 12 minutes.