1. In a large bowl or the bowl of a stand mixer, combine 1/2 cup sugar and 1 1/2 teaspoons lavender. Use your fingers to combine and make sure lavender is dispersed throughout. It won't completely turn into a powder, but this ensures you won't get clumps of lavender in the cookies. 
2. Add 2 sticks of cubed butter and beat on medium-high speed for 3-4 minutes until light and fluffy. This might take a little longer with a hand mixer. Note: You butter doesn't actually need to be softened for this! However, it will also take a little longer to get it light and fluffy if starting from cold. 
3. Add 1 teaspoon vanilla and combine.
4. Slowly add in 2 cups of flour and mix on low until just combined. Fold in 1 cup white chocolate chunks using a rubber spatula. Make sure to fold well and get any remaining flour at the bottom of the bowl.
5. Turn dough out onto a clean surface, and divide into two. Roll each portion into a 6-inch log and wrap tightly in plastic. Chill for at least 2 hours. 
6. When ready to bake, preheat oven to 350.
7. Slice each log into 12 1/2-inch pieces and arrange on a parchment-lined baking sheet. A serrated knife helps to get through the chocolate, but if you have some start to crumble, no worries! Just push extra dough back together on the pan.  
8. Bake for 10-12 minutes, until the edges just start to get light brown.
9. Let cool on pan for 5 minutes and then transfer to a wire cooling rack. Let cool completely before glazing.

To make glaze:

1. Sift 1/2 cup powdered sugar in a bowl. Add 2 tablespoons rosé wine and stir to combine. If glaze feels thick add another teaspoon wine and stir again. Keep adding and stirring as needed to get the right consistency. I like to test it on my finger and if slowly drips down, I know it's ready. If you drips very quickly, add more sugar and vice versa!
2. Drizzle glaze on cooled cookies and let sit for a few minutes to harden a bit before serving.