Cream the butter and sugar together until light and fluffy using a mixer on medium speed. This should take about 2 minutes.
Add the eggs, lemon extract, and vanilla extract and mix until combined.
Add the flour, baking soda, baking powder, and salt and mix until well blended. Mix in the white chocolate chips.
Refrigerate the dough for at least 3 hours.
Preheat the oven to 350°F.
Remove the dough from the refrigerator and roll it into balls, about 2 tablespoons each. The dough may be a bit crumbly but will become smoother as you roll it. Place the balls on an ungreased cookie sheet, leaving at least 2 inches in between each cookie. Flatten the balls slightly with your hand to help them spread.
Bake for 10 to 12 minutes or until the edges are lightly golden brown. Allow the cookies to cool for at least 5 minutes before transferring them to a wire rack to cool completely.
When the cookies have cooled completely, dust with powdered sugar before serving.