In a medium-sized bowl, combine the softened butter and powdered sugar until light and fluffy using a hand mixer.
Add lemon zest, flour, and poppy seeds to the mixture. Mix until well combined. The dough should hold together when pressed.
Shape the dough into a ball inside the bowl. Place it on plastic wrap, roll it into a 6-7 inch log, and wrap it tightly. Chill in the refrigerator for at least 2 hours.
Preheat the oven to 350°F and remove the dough from the fridge.
Slice the chilled dough into ¼ inch discs and bake for 8-10 minutes until slightly golden around the edges.
Let the cookies cool for at least 30 minutes.
Once cooled, melt the white chocolate chips and coconut oil in a microwave-safe bowl in 20-second intervals until smooth. Drizzle the melted chocolate over the cookies and allow it to set for 10 minutes.
Garnish with additional lemon zest or poppy seeds.