Preheat oven to 350 degrees F. Line a large cookie sheet with parchment paper.

In a large mixing bowl or using a stand mixer, beat together butter and sugar until light and fluffy, about 2 to 3 minutes. Add eggs, one at a time, mixing well after each addition. Mix in Meyer lemon zest, Meyer lemon juice, and vanilla extract. In a separate bowl, mix together dry ingredients. In batches, add the flour mixture, and mix until incorporated. Fold in white chocolate chips.

Divide dough in half, and shape each half into a 2-inch-by-13-inch log. Grease or wet your hands as the dough is pretty sticky. Repeat with remaining dough, leaving about 3 inches of space between logs. Bake for 35 to 40 minutes or until bottoms are golden brown. Remove from oven and let cool slightly.

When cookies are cool enough to handle, cut them into slices using a sharp serrated or bread knife. Arrange slices, cut sides facing up, on the cookie sheet and bake for another 15 minutes. Let cool, then transfer to an airtight container or zippered plastic bag for up to 1 week.